While ninty owns 33% of the pokemon company (along with a large portion of both of the other companies, creatures and GF), they are the SOLE OWNER of the IP. Meaning they can just let another studio, a new internal studio, or a new 2nd party company made by pulling out all the key people from GF (most of them are ex-ninty staff or have HIGH loyalty because ninty helped then a LOT when starting out, and I mean a LOT). SO sony wpuld just have wasted money in this case.

Not that ninty's finantial team would let this happen... if it comes to push and shove, ninty has more cash on hand than sony after all, let alone SIE.

Switch is only 3.5 times stronger than ps3, ps4 is a generation ahead ps3 so you are thinking a ps4/5 portable which is almost a generation ahead of Switch with high resolution and way better graphic setting as well as fps will consume the same electric as Switch, sure . $300 for total Switch is fine, you clearly are ignoring what i said. The $300 you said are chip only. where is buttons and analogs? Also, a Switch cart is already enough to play game, download only for multiplayer, can you tell the same with a ps4 disc only? As if bought a ps4 disc without install the data that take 60GB or above is enough already. Lack of storage can be make up by Micro SD card and it is not Vita card that take $120 a 32GB card at launch

If Nintendo made a PS4 do you think it would be a success?

Well I was told that Nin owned 33%, which technically is wrong, if the other two companies who own the other 66%, are also majority owned by Nin. That would mean that Nin actually owns well over 50%, so they would then own a healthy majority, which would also change the likely outcome if any shares were sold by the other two companies. Arguing over a topic given incomplete information is like trying to play NES being given a DS4. As for owning the rights, that doesn't mean you receive 100% of the profits, they would still be split 3 ways, 33% each. Nin would get the majority of the profits in the end, only because they own most of those other two companies.

PS4 came out over 3 years before Switch though. These new Ryzen chips came out years after X1. Newer tech, better performance and efficiency like Switch right? We've only been using price to point out overall cost so far, yet somehow you take it to mean just the chip, because it fits your argument? You mean multiplayer and DLC is a separate download, even though PS games are constantly put out at a later date with all the DLC and multiplayer included? Just like Doom which has been out long enough that all of it should be on the cart, but can't be. How do you also know that there aren't games that are just too big for the existing carts, or internal storage, that haven't come to Switch for that very reason? So only Nin can use micro SD and PS has no choice but to use proprietary storage? Nin is also red, so just orange I guess?

they wont make on scince all their dev teams are split between ps4 and vr now and not home console and handheld anymore.

You are the one who said Ryzen chip only cost $300, you didn't mention the total handheld cost $300 only. No third party are willing to use Switch 32 GB cart, let alone 64 GB or more so your argument is based on nothing. The Ryzen chip came out after X1, X3 (Xavier) also. And you have to remember AAA Western games on ps4 is 100GB or even more, ps4/4 portable can reduce it to 80 GB, yet who is willing to carry a digital only portable with several games that take over 80GB? They have to expand the storage and a small form factor handheld no way can have a very big storage outside Micro SD card. And even efficiency like X1 chip only last 3 hours for AAA games. A ps4/5 portable which is almost a generation ahead Switch with the new chip can cost only $300 as well as 4-5 hours battery life and have ps4 graphic? Wow. Not even the strongest handheld with the newest chip at the moment can do that. You know Sony can do it because you already have it in the different parallel universe, right?

One more thing, look like your "pokemon on ps" illusion and dream was already crushed by everyone

The idea behind any new Mobile, Portable, or Switch like PlayStation would be to run it on the same chipset as the PS4 or an X86/Radeon APU that is capable of running all PS4 titles without additional dev work. Basically, it would either be another version of the PS4, or Sony would provide tools to make all PS4 software run on the advanced chipset.

Even if it comes down to scaling, it would be an extreamly quick and simple process. 3rd parties have been scaling across X86/Radeon for decades, and even Sony's 1st parties are building scalability into their in house engines. This is nothing like having a PSP,PS Vita, PS3, and PS4 version of the same game, where every one has to have the game completely re-built. 

I don't even know what to say anymore. Everything purposed is based on looking at the market in 2019 or 2020. 500GB of on board flash in late 2019 or 2020 is going to be super cheap. The 7nm successors to the Ryzen 2500U and 2700U will have large gains over the current chips, as the next wave of Ryzen and Navi are both focused on performance per watt. If a PS4 Portable/Switch is built using either the PS4 APU or a completely new APU it would have elements of the unreleased Ryzen and Post Navi tech just as PS4 and PS4 Pro have had making it even more effecient. 

Also, the Switch at $300 in early 2017 was already at a material cost of ~$257. Nvidia is well known to be expensive and ruthless, as both Microsoft and Sony learned with Xbox and PS3. Additionally, even though the thread is about a PS Switch, we are also looking at a PS Portable, that would likely ship without joycons or a dock, again lowering the cost. On top of that, Sony is making massive profits on PS4 already, if this is based on PS4 Super Slim, the costs will be even lower, the R&D will be next to nothing, the dev tools, the OS, and PSN are already built. Even more so, Sony are willing to sell at break even, or even a small loss, making it even more possible to sell at $250 - $300. 

There is basically no doubt that Sony can build a Portable, Mobile, or Switch like PlayStation 4 by late 2019 or 2020. We know they already had decent success with the PSP, and completely bombed with the PS Vita (Although I would argue they killed it to focus their mobile efforts on Xperia (dumb ass move)). The only question is how successful said device would be. I would argue it would be a viable additiona to the PS4 platform at worst (~50 Million), or a huge hit (100M+). 

AAA Western can be very big, some ps4/xbox 1 games are ~120 GB, digital only mean you need a storage bigger than 500 GB or you will bring a handheld with just 3 - 4 AAA games only, not mention a dozen of small indie games which take up several GBs. And yeah, why don't you name a portable that play game like ps4 which last 4 - 5 hours and cost $250? 

Switch cost ~$260 to make mean they raise it to $300 for profit. PS4 made profit for them till mid 2014, not at launch. The dock boost over %25 power of Switch, no dock, huh? Look like this ps4/5 portable isn't compatible with PS VR base on your prediction. Also, Sony didn't sold PS4 at loss so can't be sure they will accept the loss to sell PS4/PS5 portable

No doubt Sony can built a Switch? In other word, no doubt they can copy Nintendo because it is success. Decent success with  PSP based on hardware sold, not software. PSP is one of the most pirate console of the gaming world. None game in top 10 selling games reach even 8 mil units sold. 

http://www.vgchartz.com/article/261536/top-10-best-selling-psp-games/

As of now, third parties have to make game for ps4 and optimize it for ps4 pro, make game for PS VR also. You are asking them to downgrade them as much as possible to fit on a handheld? The system you are saying will be ps4 portable, and then it will play ps5 games too, a generation ahead ps4/ps4 pro easily like nothing? Sure, if you count out Switch 2 which is also a gen ahead Switch 1 can come out that time with Pokemon as well

They dont have the type of IPs for a portable machine. Cinematic games are better suited on the big screen. That's why it works for Nintendo. There games are just more portable friendly. Games like Pokemon, Fire Emblem, Mario and many more suit the portable gaming space better.