I can see where the case for AMD could be made (the Steam Deck's APU is truly impressive), but I think Nintendo has invested pretty heavily into the Nvidia stack at this point. The Tegra boards that they made the original Switches with were left over from the Nvidia Shield; nobody was sure if the concept would take off or not. Now that the Switch has outsold the Wii, I'd imagine Nvidia and Nintendo are working very closely to design a successor to the chip, even if it's not going to be a mobile console.
Probably one the of the best things that happened to the gamedevs, console wise, was Microsoft and Sony going for x86 and AMD SoC.
What you're saying, which is true, is that Nintendo likes to cut costs and it's cheap on the hardware they use because they care more about the content for their IP, not much for the tech behind it. They could keep stretching the switch for 3/5 or more years if they wanted to.
To be fair, developers have been making games run on underspecced AMD hardware for more than a decade at this point between the XBox One and PS4, and any games coming to PC have to have AMD alternatives to CUDA physics, PhysX, etc. anyway.
Also, its not like the AAA ports have been without issues, many of them run poorly and look pretty awful compared to first party efforts like BotW. Their optimization stack might be amazing, but recycling the shield SoC AND underclocking it is definitely causing some pain.
It does seem like Nintendo has buddied up to NVidia more than console manufacturers usually do so I think its likely they stick with NVidia but I wouldn't write off the possibility entirely, especially since AMD seems so willing to please with custom solutions even for much lower volume products like the Steam Deck.
Nintendo could use one of the new Samsung SoCs with RDNA2 graphics though. Those could be pretty good competition for Tegra X* chips.
Now, Nintendo doesn't care much about that because they're into their own thing, they don't even see themselves as a tech or gaming company, the position themselves as an entertainment company.
Like, I think they see themselves closer to Disney than to Sony Computer Entertainment.
About the power profile, the switch came out with around 2h-3h battery life while gaming, depending on the game of course, I don't think it would be much of a problem.
Problem is, many existing Switch games use some nvidia-specific API (IIRC called "NVN" or whatever) instead of Vulkan.