IMO, the strategic error was AMD paying a bunch of cash for ATI, instead of an all stock deal. In 2006, with their stock near the all time high (~$40) AMD decided to borrow $2B instead. Six months later, AMD is issuing shares at $14 to meet expenses. Two years later, AMD is trading at $1.50, and on the verge of bankruptcy. In retrospect, AMD's outcome could have been vastly different if they had done the all-stock deal in 2006, or even issued shares instead of borrowing.
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.
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.
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.
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.
A few of these are pre-acquisition but the GPU's for the xbox 360, Gamecube, Wii, and Wii U were all ATI/AMD as well.
I'm sure at this point more console hardware has been AMD than any other manufacturer.
Also if we look at the latest gen, there's some pretty cutting edge architecture and manufacturing processes used in the new xbox/playstations. Zen2 is no slouch.
Historically it was (when AMD was drowning in debt from the acquisition and had no competitive processors on the timeline), but is this still true? For instance, all of the major game consoles (ps4/ps5/xbone/xbox series x/switch) use AMD boards, and as I recall, those deals lifted the company's financials quite well.