I don’t think a device necessarily needs a BotW style system seller at launch (obviously it doesn’t hurt) but rather a steady flow of desirable games. As for MK7 not being a system seller while MK8 is seems like revisionist history. MK8 couldn’t make Wii U sell well and didn’t go on to sell massive numbers until it came to Switch. A game can only do so much if the hardware is undesirable.

Also, I don’t think Mario Kart 7 would be the same game that we got on 3DS in this alternate timeline. In our timeline we got MK7 in Dec 2011 for 3DS & MK8 in May 2014 for Wii U, in this alternate timeline it’s very possible we got MK on Vita level hardware in late 2012/early 2013 and fall somewhere in between MK7/MK8 in terms of size/scope. The same goes for other franchises that got 3DS & Wii U entries relatively close to each like Mario 3D Land/World or NSMB2/U.

I don't think Vita level hardware would look very good on a TV either circa 2012, even Miyamoto said HD is important, by 2011/12 everyone and their grandma (literally) had a HDTV ... to have a "console" that only outputs at like 540p (sub HD resolution) would be another blow against it.

The concept just wasn't ready for prime time in 2011/2012. Mobile chip tech just wasn't there yet. The console side experience especially would've been quite underwhelming.

The other thing is it would have likely cost $250-$300 with mostly the 3DS library ... and take a gander at how the 3DS was selling at $250.

It basically would be a more powerful version of the 3DS with TV output, but I suppose minus the 3D screen quite probably. The Tegra 3 was still a very new chip circa November 2011. 

As Conina already said, offscreeen tests are what is really measured, since onscreen measurements, beside being locked to refresh rate, are in different resolutions - that's why actual VS benchmarks are always done offscreen in the same resolution, and this is where SoC can be pushed to limits under same conditions.

Well, Vita level hardware would probably be just barely able to pull it off - default Vita resolution was 960x544. So let's take Borderlands 2, as the example of the game I remember that was ported from home consoles - it runs in this resolution, but not terribly good. Once you lower resolution to 720x408 (like a lot of other games used) it runs with locked 30fps on non-overclocked Vita. If you had Vita dock, that lets Vita overclock quite a bit while docked and additionally cooled, it's just might be possible it would hit 1280x720, which would be enough for TVs of PS360 era (not that even all the games on PS360 ran in 720p, especially later in the cycle).

But yeah, overall, I don't think tech was quite there yet, for all 3rd party support Switch got. On the other hand, if they cared just for their own games and some of the 3rd party support (especially indie games), I'd say, technologically, it was quite feasible.

The audience for motion controls hasn't gone away, they're still a popular feature in many games on Switch including some of the highest selling ones like Splatoon 2 and 3, BOTW, TOTK, Mario Odyssey, Super Mario Party, Luigi's Mansion 3, etc.

Switch Sports and Ring Fit Adventure are built around them and they have both sold over 10 million copies on Switch.

This is next level copium. Wii-like titles sold over 100 million units in a 90 million userbase 

The sames titles on Switch are still unable to cross 30 million in a 140 million userbase 

The audience who was driven primary by motion control games is mostly gone

None of the other games you listed are motion controls intensive. Indeed you can turn them off entirely in all the games you listed and the experience will be the same (actually better as motion controls sucks, but I digress)

No Wii game "sold over 100 million on a 90 million userbase", and it sounds like the title you mean here is Wii Sports, which was bundled with almost every system, so not a useful comparison point against games that are largely sold standalone. Sales do not scale linearly with install base anyway; PS2 sold over 150 million yet only a handful of games on it passed 10 million copies sold.

Motion controls are the default control scheme in BOTW, TOTK, Splatoon 2/3, Luigi's Mansion 3, etc and they are how millions prefer to play.

If the audience for them was gone, games like Super Mario Party, Ring Fit, and Switch Sports would have flopped as motion controls are mandatory in those games, yet they sold over 20 million, over 15 million, and over 10 million so far respectively. All three of them actually sold better than Wii Party on Wii, and SMP sold better than all but 7 games on Wii. (And is on track to pass the next two in line, Wii Fit and Wii Fit Plus)

Motion controls are alive and well and here to stay.

 I meant over 100 million units combined among all wii-like games, if you want to include Wii Sports then it's close to 200 million. As this was excluding Mario Party, as it's a long franchise that was already successful without motion controls 

The Switch games where motion controls are integral part of gameolay are few. Ring Fit, Switch Sports and 1-2 Switch. They have sold roughly combined 30 million units which is less than a third of how much Wii games sold

I never stated they need to scale linearly, although Switch sells consistently more games than Wii the motion controls focused software sales have decreased substantially despite being available for a much bigger userbase 

You just need to take a look in the top 20 best selling games for each system to be sure how much motion controls have fallen. Even all the best third party games in Wii were all Just Dance, a game that heavily favored motion controls 

Of course there is always be audience for certain kind of games, but they are no longer enough to hard carry a system like they did in Wii days. For most of its players motion controls were just a fad

So you know that the number of games was higher on the Wii, but still act as if a third of the sales across fewer games on Switch is bad.

The Wii wasn't carried by motion controls in the way you imply either. But it's nothing new that the prerequisite for the fad argument is dishonesty.

Looking at the top 10 selling games for both systems and like more than half for the Wii are motion games, whereas for the Switch it's not even close to that. Mario Party was a big selling IP established long before motion controls were implemented into the IP. 

Wii Top Sellers:

1. Wii Sports (82.9 mill)

2. Mario Kart Wii (37.3 mill)

3. Wii Sports Resort (33.4 mill)

4. New Super Mario Bros. Wii (30.32 mill)

5. Wii Play (28 mill)

6. Wii Fit (22.67 mill)

7. Wii Fit Plus (21.13 mill)

8. Super Smash Bros. Brawl (13.3 mill)

9. Super Mario Galaxy (12.8 mill)

10. Just Dance 3 (9.92 mill)

Switch:

1. Mario Kart 8 Deluxe (60+ million)

2. Animal Crossing: NH (44.79 mill)

3. Super Smash Bros. Ultimate (33.67 mill)

4. Zelda: Breath of the Wild (31.67 mill)

5. Super Mario Odyssey (27.65 mill)

6. Pokemon Sword/Shield (26.17 mill)

7. Pokemon Scarlet/Violet (24.36 mill)

8. Super Mario Party (20.3 mill)

9. Zelda: Tears of the Kingdom (20.28 mill)

10. NSMBU Deluxe (17.2 mill)

Lets be honest too, Ring Fit was likely bolstered heavily by the pandemic shut downs that closed gyms everywhere around the world and drove the home fitness category through the roof, look no further than Peloton that had sky high sales during the pandemic and has crashed since lock downs ended. 

Switch Sports has sold a respectable amount but it's currently only the 18th best seller on the Switch and probably soon to be overtaken by Mario Wonder. Compared to what Wii Sports/Resort were on the Wii (no.1 and no.3 top sellers), it's well below that.