I'd say it is mostly due to the fact that Nintendo has never had a home system sell like this before. Handheld consoles have lower attach rates, while the Wii sold a lot to non-gamers who bought casual games and not core Nintendo IP.

They've literally never had a home system sell like this before whose user base was mostly gamers. That, combined with the fact that many of their main IP are considered the best or among the best in their respective series: Odyssey, AC, Zelda, MK, Smash. Also since new AAA third party games have left Nintendo in favor of pushing graphics Nintendo first party games have now become the main drivers of system sales. The Switch library is mostly Nintendo games, indies, and older third party games that are bought for the ability to play anywhere. This all increases the amount of sales of big Nintendo games per owner since third parties don't put serious effort into taking a piece of the Nintendo gamer pie. Basically Nintendo first party games are like what GTA, CoD, and Fifa are to Playstations, in that the audience has been cultivated to all enjoy those games so they become the mega sellers, but unlike CoD and Fifa where you get a yearly release to buy a new iteration of the same game each year, you get one or two games in each series per system from Nintendo so they sell for years as evergreen titles.

Summary: it's a combo of best selling Nintendo home system ever that focuses on gamers, some of the best versions of each series, and third parties handed the reins over to Nintendo for them to dominate software sales alone.

I mostly agree with what the OP has said, but I'd probably put it a different way.  Here is what is driving sales on Nintendo IP.

1) For any new iteration in a series you can expect about 25% to be disappointing, 50% to be solid but not exceptional, and 25% to be exceptionally good.  Most fans consider Zelda, Smash and Animal Crossing to be exceptional on the Switch, and that is why they are selling far, far beyond what they ever did before.  However, Pokemon is considered disappointing by most of it's fans and it is still selling better than the 3DS Pokemon games, so this is clearly not the only factor.  

2) Mobile games are marketing certain IP.  These games give people a taste of the core experience and some people decide they want the whole thing.  Pokemon, Fire Emblem, Mario Kart, and Animal Crossing all have mobile games and these are giving these IP a boost on the Switch.  So when you get a game like Animal Crossing that is a) exceptionally well made, b) is marketed to the mobile audience, and c) comes out right at the beginning of a quarantine then you have a perfect storm of explosive sales.  This is also why Nintendo needs to make a proper 2D Mario to go with the Mario Run mobile game.  However, it doesn't explain Zelda and Smash which don't have mobile games.

3) Consolidation.  Having software consolidated on one platform helps a lot with a steady stream of software releases, but that still isn't the most important part of consolidation.  The most important thing is the consolidation of the customers.  Smash Bros was released on both the Wii U and 3DS and that kind of split the fan base.  On the Switch they can make a better game, and all Smash fans are on the same platform.  Home gamers can now play Pokemon and handheld fans get games like BotW which is so much larger in scope (and better) than any original Zelda that appeared on a handheld before.  Both home and handheld gamers get the best of both platforms.  Naysayers say, "What is Switch going to do without AAA third party games", but Switch actually is getting extra AAA games simply by combining home and handheld in one platform.  Home gamers never got an Animal Crossing game that sold anywhere near 10m, but now they are getting one that is on track to sell 40m+.  (While the PS4 doesn't have any game that sold that much on it's platform alone.  How does it sell without Animal Crossing and Mario Kart?  I digress.)  That is where Nintendo is getting it's AAA games.  Nintendo is bringing extra heavy hitters to both home and handheld fanbases just by combining them together.

I see the Wii very differently, it wasn’t Nintendo abandoning traditional gamers, but rather a return to form after abandoning their traditional appeal during the N64. At least on their home consoles. The return to prominence of Super Mario on the Wii is a big indicator of that, since the Super Mario brand was BY FAR traditional Nintendo’s biggest brand.

There isn’t much of difference as to why Wii Sports and Breath of the Wild/Animal Crossing sold well. These were big killer app experiences that people have seen as compelling.

The Switch is a continuation of the Wii’s revolution as its basically a hybridization or a Wii style console and an ultra-advanced handheld - which is the key reason for the added popularity of mostly everything: the greater convenience makes Nintendo-style games more compelling on Switch. And so you’re getting a combination of games that sold well on Wii and DS.

Animal Crossing saw a fairly huge bump because of its incorporated sandbox elements, and it’s basically taken what appealed about the older versions of the game and come as close to perfecting the experience for a market audience that has ever been done.

Had Splatoon been around for the Wii, no doubt it would have been a major hit.

The real explosion title is Breath of the Wild, and that’s no secret, it is the first really exciting Zelda release since Ocarina of Time. While Ocarina of Time was great, it still felt short of original expectations. Breath of the Wild is also a return to form for that franchise as it fulfilled what many were expecting Zelda to do when Nintendo moved into the 3D space: explore a vast and open world, and stare down upon it from the top of Death Mountain.

In short, to me the Switch feels A LOT more like the continuation of the Wii in the same way the SNES was the continuation of the SNES. The Wii/DS fanbase is the driving factor for Switch’s fanbase in the way the NES fanbase was the driving factor for the SNES. Except Nintendo is treating Switch a lot better than they did the SNES, so it has more potential.

Games are selling better because: A) the games are really compelling because of their quality. B) Hybridization makes a very convenient console that people are more likely to want to play games on. C) Nintendo is building on their Wii/DS base, and the Wii/DS crowd, which included LOTS of children and teenagers are now in their twenties and thirties. And those of us from that fanbase who are a little older have families now with new children old enough to play games, and we’re using the Switch as a family console.

Rol, Liquid and Jumpin summarize all good points.

Case closed here. 

1. Nintendo Switch is the successor of 3DS, Wiiu, and Psvita. Major market here

2. Nintendo uses cellphone games like a trojan horse to boost console sales.

3. Nintendo Switch is back to Wii/DS route and games have back to the roots, a good example is Zelda. 

4. And, Nintendo all ages of arcade culture is a great fit for the actual company direction. 

1. Size of the Userbase
2. Quality of the games
3. Userbase is comprised mostly of gamers, not casuals like on the Wii
4. A great diversity of games. There's something for everyone and they come with great new ideas or mechanics and it's not all the same stuff (aka either a Action-Adventure, Action-RPG or FPS that all work by the same formula)
5. Not screwing over their players with endless monetisation schemes like EA, Activision and the like do. Basically AAA games without the drawbacks.
6. Less competition from AAA games because they expected a Wii U 2 desaster and are now scrambling to get on the hype train.