Vita TV was for playing handheld games on a TV. Switch games are not designed just for handheld. In most cases it usually prioritises docked performance. Even if you're one of those who tries to belittle Switch as a handheld that plugs into a TV, the games themselves are primarily designed to be played on TVs as console games.

Ever since the lite, it has to be assumed that a Switch TV is somewhere in the files.
Whether or not it gets actioned on is another story. There’s at least a corner (if not a whole side) of the market it would appeal to. It could also be a nice entry level unit for prospective Switch 2 owners who want a temporary and less functional unit to start building a software library on before committing to a full priced next generation hybrid machine.

I believe this echoes some of the thoughts above.

Actually we had a Switch-only Mario Kart, Mario Kart Live: Home Circuit, is it a good Mario Kart, eh. I will also say that the DLC to MK8D was the equivalent of making Mario Kart 9 since is doubled the amount of tracks. So I'll give Nintendo that.

And yes we haven't had a StarFox release, but we haven't had any clues that let us know that Nintendo still cares about that franchise, along with many other forgotten franchises. The only thing I can see are the easter eggs from The Super Mario Bros. Movie. Other than that there aren't any signs that can give us hope for a new addition to the StarFox, Rhythm Heaven, Earthbound, Kid Icarus, Mario Superstar Baseball, StarTropics, FZero, and WarioLand series' for the Switch.
Golden Sun was given NSO treatment recently, so it shows that they acknowledge its existence, though a very delayed acknowledgment. But all the others except Rhythm Heaven, Mario Superstar Baseball also have NSO releases.

Sadly we may never see new Switch-releases for those franchises.

That's awesome that you still have a N64!

If all these franchises are given a new addition for the Switch, I can see it selling some hardware units to the older generations.

The screen, the dock, the battery, possibly a smaller box saving in transports... I imagine that Nintendo would prioritize profit over numbers sold, so I don't see it happening either, especially since they've had more than enough time to release it.

Just looking at the past, we've seen Nintendo release console revisions once the successor releases.
Wii mini: Dec 2012, 1 month after WiiU released
SNES-101: Oct 1997,1 year after the N64 released
New Famicom: 1993, 3 years after the SNES released

So why can't we get a new revision for the Switch after the successor releases? Especially if they can produce a simpler revision with less components, like the idea of a Switch TV.

How much would you think they would sell it for?
It is about $257 to manufacture a Switch.

Really depends of the game tbh. Pokemon and Animal Crossing are designed for handhelds I think, so is Clubhouse. Link's Awakening is a remake of a handheld game so...

I'd say Mario Kart and 2D Mario are designed to be played equally on both formats. I will put Monster Hunter in this category too (I know it's a third party but it's still a major seller). 

Smash and Splatoon are for TVs imo, but also have a strong local competitive in mind with goes well with handhelds (remember you would otherwise need two TVs) 

3D Zelda, 3D Mario and Minecraft are mostly for TVs 

Ring Fit and Switch Sports are 100% designed for TVs

So... I don't think there is a hard rule here. RPGs (like Octopath Traveler, Fire Emblem), 2D games, simulation games are all very well suited for small screens and handheld play 

There is no such thing as a game designed for portable or console play. Any game can be played anyway you want. Portable platforms are just smaller screens than your TV screen. Some games may be more comfortable to play depending on your setup such as first person shooters being more comfortable to play on a larger TV screen or a card based game being more comfortable on a smaller screen with a touch screen but the beauty of Switch is being able to pick and choose. Yugioh for example feels far better on a small touch screen but that doesn't stop me from playing on my TV or Overwatch on the TV feels better yes but being able to play in my hands while watching television is very convenient.

$257 to manufacture a Switch? That is more then I expected. There are also logistical cost to consider to get the console to retailers and obviously retailers would like a cut.

With this kind of manufacturing cost it's hard to believe Nintendo makes a profit on the console, but I always thought they did.

Given Nintendo operating profit of 30%+, I would estimate they make 10-20% profit on their consoles. On a Switch that would be between $30-60.

What? Is that the old switch model ?

The $257 figure was from April 2017. Even with inflation, I'm struggling to comprehend that Switch is still $257 or so to make in 2024. If it is, no wonder Nintendo won't drop the price. 

With the latest shipment figures from Nintendo putting Switch at nearly 140 million shipped (a million or two above what I thought), Switch really has a good shot to surpass DS, and maybe PS2. We'll see.