Prediction time !

The 3rd Switch successor to the Switch 2 will be called the " Nintendo Switch 3D" ;)

I would not be against it.

I enjoyed the 3D display on the 3DS, it's a unique gaming experience that hasn't really been duplicated to the same effect anywhere else.
If it was a brighter, higher resolution, HDR, OLED, 3D panel, that would look glorious...

Obviously having the option to turn it off would be a must for other users.

Found some benchmarks from way back, iPad 2012, which has same GPU as Vita, vs Asus Transformer, which has Tegra 3

https://www.anandtech.com/show/5688/apple-ipad-2012-review/15

It would have flopped, or sold decently depending on how much Nintendo was willing to operate at loss to keep their market share 

The biggest culprit is handhelds owners. Handheld owners are the true majoriry of Nintendo audience 

250 USD is a steep price increase from DS owners. Remember 3DS was released in was 250 USD and Nintendo needed to cut the price quickly. The problem here is this system would be much more expensive than a 3DS to manufacture so either Nintendo would take a huge loss for years or they would be adamant in decrease the price resulting in millions of units lost 

Slightly above 3DS graphics would not make console owners from Playstation, PC and Xbox to embrace this new handheld either. The lack of HD developed games like BOTW and Odyssey would hurt Nintendo a lot here. Most Wii U games would be even more uneventful if they were bound to have slightly above Game Cube level of graphics. For home console they would have kept the game Wii-like games as their system sellers would be their biggest disappointment 

Wii owners love to brag about how fun was to play with motion controls but the truth is the audience for this kind of game faded quickly, as Xbone proved with their kinect 

With the focus in Wii-like games and high price point throughout all its life I could see this selling in Xbone range at best

Otherwise, if Nintendo moved away from Wii-like games and investing in quality console games and decreasing the price of the console I could maybe see this selling as much as PS3

Either way, the existence of this console would have hurted Switch itself. As it would probably mean Switch was going to launch in 2019, much closer to PS5 and Series X. Without much time to have a breath of exclusivity in the market and not serving as an auxiliary device anymore. Plus it would be the first Nintendo system with HD games, hence most of Wii U games would only see the light in this system. Switch would have much more trouble passing beyond the 100 million mark

It's not the same GPU as the iPad.

Vita used: PowerVR SGX543MP4+
iPad 3rd Gen: PowerVR SGX543MP4
iPad used: PowerVR SGX543MP2

The "MP4 and MP2" denotes how many cores they have for the graphics chip.
The "+" signifies some customizations to the core for Sony.

So whilst they share the same graphics core architecture, there are differences.

Asus Transformer is also not the most optimized or updated variant of the platform either.

Yeah, I know what MP stands for, should've said "has about the same GPU as Vita", since, obviously, Sony did some customization to 543MP4. And even if not, if anything else, I think Vita has dedicated VRAM.

Point of those benchmarks is mostly in comparing 543MP4 to Tegra 3 in real life examples of similar products (with former easily dominating Tegra 3) - and Vita, packing 543MP4+, is probably best you can hope for out of handheld from that time, so Nintendo's a la Switch handheld doubtfully would be  as fast, unless they actually made something like Vita as well. And while Vita was able to pull some impressive games (and even some ports), I don't think that PS360 to Vita difference was as low as PS4XBO to Switch, so any Nintendo's Tegra 3 based "hybrid" would fair even worse.

Vita certainly does have dedicated VRAM. 128MB. But it's only 3.2GB/s... System Ram uses Samsung 256MB LPDDR2 at 1ghz chips so we are probably looking at around 2.4GB/s.

Tegra 3 can accommodate up-to 2,048MB LPDDR3 Ram at 6.4GB/s. Massive difference.

Anything that uses lots of heavy textures, alpha effects and higher resolutions, the Tegra 3 would pull ahead of the Vita, it's simply a better environment for that kind of work load.

Although the Vita with it's tiled based deferred renderer can punch above it's numerical weight... Which is not something that Tegra adopted until Kepler if I recall, maybe even Maxwell.

We also need to remember the development environment back then, nVidia's API's and drivers were far less mature than PowerVR's and the development environment tools were rudimentary at best, it's not the case these days, it's helped that Android has matured.

We also need to remember that in non-offscreen benchmarks, Tegra 3 is very competitive with PowerVR. Offscreen has never been Tegra's strong point.

Just noticed I've posted Egypt Offscreen twice, instead of  (intended) Pro Offscreen - fixed that.
iPad 3 (with MP4) is well above Tegra 3 even more in that one (3x as much, vs "only" 2x in Egypt)

If you look at other test at that page, you'll see that Fill and both Triangle tests also go to MP4 by a wide margin. Admittedly, I don't know about the power usage, so doubt it's been tested at the same wattage, but whole point was and is that Vita packs much better hardware than potential Nintendo's Tegra 3 based "hybrid" would, and still isn't as close to PS360 counterparts as Switch is to PS4XBO - so Nintendo's handheld would be even further away.

The point I am trying to convey is that the development environment for Tegra 3 was very immature and it can be a far more memory-rich environment which was a bottleneck on other SoC's.

There was no low-level nVidia based API's like there is with Tegra X1 and the SDK's were very immature.. Obviously in a closed environment like a console a lot of those overheads can go out the window.

Also... We need to remember that the Transformer Prime originally came with DDR2-500Mhz Ram. Not LDDR3-1600Mhz Ram.

Bit of a difference there that held the GPU back in the original prime... 2GB/s vs 6.4GB/s. So it's obvious it's going to come up short against the MP2 because of that, let alone the MP4.

Could a docked configuation with higher clocks and memory bandwidth a la the real Switch give a Tegra 3 powered device the push to outperform Vita by a significant margin?