I have seen both statements emphatically made multiple times on this site with regard to Nintendo hardware.  Which is it?  First, it was repeatedly stated that the rise of mobile phones had eaten so deeply into the handheld market that dedicated handhelds post Nintendo DS and PSP were doomed.  While the Vita flopped due to a rapid lack of support from Sony, the Nintendo 3DS sold close to 76 million units over a 9 year lifespan.  Yet even still, due to that number being less than half of DS lifetime sales, it seemed to support that mobile had taken a massive chunk of the dedicated handheld market away for good.  Which led to a prediction made here that no dedicated gaming device outside of the Sony PlayStation family would ever surpass 81 million units sold ever again.

Fast forward to March 2021, and the runaway train success of the Nintendo Switch which has already surpassed the lifetime sales of the 3DS, and will soon pass the PSP and Gameboy Advance as well.  Many on this very forum attribute the success of the Nintendo Switch purely to its capability to be used as a handheld.  But how can that be true, if mobile phones already killed the dedicated handheld market, a market which has been shrinking for years?  If the Nintendo Switch is a device with "only portable appeal" as so many have labeled it, why is it about to surpass what was viewed as the ceiling for the dedicated handheld market?

Much more than a portable device, the Switch is a hybrid console (the original model anyway).  Whether people like to admit it or not, the system has appeal to console gamers who play it on their tv as well as take advantage of the ability to seamlessly continue their games on the go.  But even still, with the failure of the Wii U, it had been stated that the "core" Nintendo base had been arrived at.  Around 14 million who would buy any console Nintendo puts out, and around 76 million handheld users who would do the same.  This reasoning led to a belief that even as a hybrid system, the Switch couldn't possibly sell more than 90 million units.  Which is something that it is already poised to do later this year.  The fault in this reasoning assumed that Wii U owners and 3DS owners were primarily separate groups, and that combining their numbers would represent a ceiling of Nintendo's potential audience.  But, Nintendo has shown that when they successfully innovate (the DS, Wii, Switch), they are capable of reaching a broader audience.  Besides, anyone who points to the existence of the Switch Lite, which can only be used as a handheld device, as proof that the Nintendo Switch as a whole should be viewed as "just a portable device", needs only to look at the sales of the 2 models.  The original Switch which can be docked for home console play released 4 years ago and has never received a price cut.  It costs $100 more than the Switch Lite, yet it regularly sells out even when the Lite remains available.  If the Switch only has portable appeal, and "very few Switch owners use it on their tv", why would the version priced $100 more sell out first?  Why would the version that is more expensive due to its "least desirable feature" sell out first?  The answer is because the Hybrid nature of the system is its "most desirable" feature.  

The next reasoning for the Switch's increased success especially following the monster hit release of Animal Crossing last year has been assigned to the Covid boost.  Which seeks to explain that family stimulus checks are being spent to buy Nintendo Switch's in unprecedented numbers to give people something to do during lockdowns and social distancing.  But, why would the one gaming device on the market that is supposedly only desirable for its portable aspect be so sought after in a situation where people are home in front of their TV and computers more than ever?  Why didn't Google Stadia take off instead?  Or Oculus Quest?  Or why didn't the 100+ million PS4 owners who passed on PSVR use their stimulus checks to give that a try?  If the Switch is a device whose most desirable function is to be take on the go, why did it explode in popularity during a "social distance and stay at home" pandemic?  The Switch online does not have the robust chat and social features of other devices, so why was it so sought after over devices that would better cater to this in a time where people are trying to fight isolation?

Sorry for my tendency to rant or go off on tangents.  But feel free to discuss any of the points I have made.  But, especially remark on how the Switch could be viewed as successful solely due to portability in an era where mobile phone gaming was supposed to have already killed handheld gaming.

Neither.

In addition to several factors already mentioned in this and other topics, it is worth remembering that this is Nintendo's first home console (albeit a hybrid) to receive a canonical Pokémon game - a franchise that has a very loyal audience. That alone may have guaranteed between 10 and 15 million more potential consumers for the Switch.
Another decisive software for the console's success was Zelda: Breath of the Wild, which attracted several gamers who like open-world games like Skyrim and The Witcher 3 (which, incidentally, had successful ports for the Switch).

You make some interesting points. The Switch Lite really does raise some serious questions about the belief that a dedicated handheld can no longer succeed in a market that is saturated with smartphone gaming. I think the "threat" of smartphone gaming to Nintendo might need to be re-evaluated for the new decade. It was certainly the case in 2014 and 2015 that the 3DS was having its lunch eaten by smartphone gaming. Heck, even Nintendo started releasing a few smartphone games back around that time to placate their shareholders. The 3DS was also selling really well until around the latter part of 2014 when its sales clearly started limping along. Really, the only reason why the 3DS even made it to 75 million was because Nintendo kept it on life support for so long. Most folks on VGChartz would have told you in 2015 that the 3DS wouldn't even make it to 70 million.

Smartphone gaming had the day when it was stealing Nintendo's casual audience who bought the Wii and DS.  That said, this fad has significantly died out and I think that it was a microcosm of the same video game crash that occurred in the 1980's and Nintendo is now once again the beneficiary of that fallout. In the 80's the video game market got saturated with so much garbage that people just completely got turned off gaming. Nintendo then came in with their Official Seal of Quality which assured gamers (and parents) that what they are buying will at least meet a minimum bar for quality and they basically stole the entire market. From what I understand, the same thing might have happened to smartphone gaming with the insane use of microtransations and the general lack of quality of control that became commonplace. This diminishing quality played right into Nintendo's hand and may have created the conditions for the massive swell in popularity that we are seeing for the Switch right now. Nintendo not diving in head first into smartphone gaming like a lot of people were saying Nintendo needed to do 5 years ago might be what actually saved the company. Nintendo had enough foresight to remember the 1980's and what made Nintendo super popular in the first place.

More than 100 years of flukes 

Mobile haven't killed handhelds, just moved away the crowd who were never console gamers in first place. That's why there is no demand for games like Nintendogs and Brain Age on Switch, you can find 90 different better versions of those games on Google Play and Apple Store without spending 300 USD in another device

Switch is just a good enough system to convince people it's a worthwhile purchase to play games. It has attract Sony consumers, Xbox consumers, PC gamers, Nintendo's gamers and even non-console/PC gamers. For most gamers it's completely pointless to have Playstation, Xbox and PCs in the same generation when almost all the best selling games are shared but completely acceptable to have one of them plus a Switch 

And in Asia seems like makes sense to ONLY have a Switch as they don't even care for the best selling third parties existing in Playstation or Xbox

Mobile shrunk old fashioned handhelds dramatically, there's just not much arguing

DS (150 million) + PSP (80+ million) going to 3DS (77 million) + Vita (15 million). That's a massive reduction.

Switch isn't a traditional handheld though even though it can function as such if need be. It's a portable console that can run fairly high end games including Nintendo's home console lineage of games. So that is a difference.

People associate portables like 3DS and Vita with smaller scale, non-console type games almost exclusively and those skewed too close to mobile gaming's territory. 

Yeah, I've always believed that myself about the mobile market.  The people who spend their time on free to play games aren't the same as the consumers in the dedicated handheld space.  Anecdotally, I used to have a co-worker who would play Candy Crush on his work PC, but would rib me for talking about actual video games on consoles and handhelds (and we were the same age).

I don't doubt that there was a Covid boost in early 2020, I just have my doubts that the Switch's sustained sales throughout the year are owed solely to that.  And as I mentioned, I find it odd that devices that center around the living room and internet access got less of a boost throughout the year during a period of lockdowns and social distancing, than a piece of hardware which features the ability to leave the home.

Vita and 3DS also had substantial problems.
3DS began with a massive anti-3D propaganda blast that said everything to glasses free 3D damaged eye sight glasses-free 3D caused aneurysms. Vita and 3DS were both impacted by pricing themselves out of range of consumer demand - although 3DS fixed that.

Switch merges home console value with handheld popularity.

And the person above who said motion and casual gaming is no longer in fashion: Animal Crossing: New Horizons and Ring Fit Adventure say hi. The big issue with casual and motion gaming is not that people don’t want them anymore, it’s that most of them are below the quality they should be for the 2020s. Animal Crossing is a great example of how Nintendo brought more robust depth and features without increasing the necessary daily time investment from previous games - that’s what makes a great casual game, giving the player the option to check in for a few minutes, but also allowing them to play all day if they want: the main goal is to keep them coming back over a long period of time.

If you ask me, the fact Nintendo is so low, currently, on quality software that gets players off the sofa and on their feet is a missed opportunity in the era of COVID quarantines. Ring Fit Adventure is the most frequently sold out game in the Switch’s library.

I will say on the first point, if mobile killed handhelds, it's mostly baloney. Even with the 3DS selling less than other Nintendo handhelds, it still sold 70 million units. And really, the poor performance of the 3DS was due to issues with the 3DS, not handheld in general. Moreover, I'd say handheld gaming is in a better spot that mobile. While there are certainly a lot of mobile games that do well, most are gacha games. Really, you can only make a few kind of games on phones (which is a major problem Nintendo ran into). I think the problem with the statement "mobile killed handheld," is that the analyst in the industry have a problem at looking at the industry in totality. First, mobile was still new so a lot of the games could do well because it was an uptapped market. This declined when it became clear that people on mobile don't want to spend money (kind of a prerequisite for any market). Second, PSP Vita was doing poorly and the industry has a bad Sony bias. If Sony didn't leave the industry, it would still be talked about. Aside, but this is also why everyone missed the Switch because no one bothered to look at Nintendo's handheld sales.