Due to form factor and size.. 720p for power/performance and compatibility. That res on a screen of that size good enough for most users and going 1080P would be a bit overkill. Also would drain battery more considerably.

Fyi a 720p screen would be 209.8 PPI. This is almost double of that of a 27" 1440P monitor. Granted that you'll be viewing it closer, this is a good sweet spot for portable performance.

I just want a cheep non-portable system to play the few good exclusive RPGs Switch has.

Nobody have forgotten I hope all these insult received when we were a few 2 years ago to say that there would be no "Switch Pro". I was one of them so I have not forgotten.
A similar Switch a bit larger with a OLED screen and a few battery saving optimizations are not a "Switch Pro". It is just a little SKU variation to maintain a fresh catalogue of products.

Definitely 720p. The drawbacks of 1080p simply aren't worth it on such a small screen (let alone smaller screens, e.g. phone screens). I'd probably still play some games in 720p on my PC if it didn't mean a blurry picture on my 1080p screen. If there's one thing that CRT monitors did better, it's adapting to different resolutions.

If it can output at 4K in docked mode, it is absolutely more capable than the regular Switch, therefore it should be able to bring games at greater resolutions and performances. To me, that just sounds like the PS4 Pro or the New Nintendo 3DS. 

It will never be 1080p, not until a full new system. Most big games don't even run at 720p so it would be overkill to have a 1080p screen knowing most games won't run at that but at 720p anyway.

Unless you are also an active Switch developer, I'm going to defer to MVG's knowledge of the situation. 

While I am not an active Switch developer, I am a programmer, which I why I think it would be fairly trivial for Nintendo to do this. When games switch (no pun intended) to their docked mode, it's really just caused by the USB-C connection inside the dock saying "yes, you are connected to a TV now", which puts the Switch hardware into its higher-clocked modes and tells games to run in their docked graphics configs.

So, again, Nintendo doesn't obviously need a physical USB-C connection and a dock to tell games to use that config. They could just tell them anytime at the OS level.

How efficient is that? And how much would that cost compared to what MVG is saying?

I mean, it wouldn't cost anything? What post did MVG say all this in? I would like to read it.

Again, all of my speculation is based on Nintendo contracting NVIDIA to make a new, much better SoC for it. People don't realize just how awful the current Switch SoC is - and I say that as a huge fan of my Switch. But from a hardware-only perspective, Nintendo took an already out-of-date mobile chip, not known for being very efficient or fast (hence why no mobile phones really used it and NVIDIA started using their stockpile for the Shield system), and made it worse for the Switch. The Tegra X1 that is in it has 4 x ARM Cortex A57 cores, another 4 x ARM Cortex A53 cores, and a GeForce "Maxwell" era GPU with 256 CUDA cores. But for the Switch, Nintendo disabled the four Cortex A53 cores, and downclocked the GPU and remaining CPU cores severely in order to get decent battery life out of it.

If Nintendo asked NVIDIA to do a modern "re-do" of it, I could imagine it being 4 x ARM Cortex A78 cores, and a "Ampere" based GPU with 512 CUDA cores, built on Samsung's 8-nm process. Those specs could then run at VERY low clockspeeds, like 1 GHz for the CPU and 1GHz for the GPU, while still WAY outperforming the current Switch in its docked mode, and only consume probably like 2 or 3-watts of power. For reference, again because the Tegra X1 was never very good to being with, the Switch uses 9-watts in portable mode and about 16-watts while docked. That would mean my theoretical SoC above would be giving better battery life while running Switch games in their higher graphics modes. Now, some of that battery life increase would go back into the 1080p display, but even still, it would probably be a +30% more longevity over the current model.

Nintendo doesn't typically spend a lot in the R&D department, but one would hope that with the runaway success of the Switch, Nintendo would be smart to invest at least some of those profits into a big SoC upgrade.