Odd reasoning. In my experience the larger a company is the more it is comfortable turning down low margin deals, and consoles are low margin by Nvidia standards. The shrinking or small company is the one that will bend over backwards to please partners with custom solutions that take development cost for low end margins. I mean, have you worked for a large and small company both?
Heck, let's get away from the theoreticals, Nvidia very much likes making turnkey solutions with finalized hardware while AMD made semicustom a big part of their business model. They're large because they make good hardware, and they're getting a lot of VC funding for deep learning and automotive right now, but they're not selling as much custom hardware as you theorize, your example isn't an example, a stock valuation doesn't prove your point. The Switch TX1 is literally a TX1, see gif above.
Semicustom is literally in AMDs business model, they have to for survival; Nvidia will do it but there would have to be big margins in it at the end.
https://www.amd.com/en-us/solutions/semi-custom
This isn't to say that's the reason we think they're going AMD, rather it's the closely compatible APU solution, staying on x86 which Nvidia can't do (without a miracle collaboration from Intel), and the leaks from people who have broke previous hardware before pointing to AMD super_secret GPU code. Nvidia would mean ARM which would mean a clean break, and there's currently not many ARM cores outside of Apple and high end server makers that compete with Zen.
This isn't the Neogaf reality...It's just what most evidence points to so far. If its Nvidia colour me surprised, as I haven't seen any proof of it outside of an odd argument for its stock value and neogaf maybe not being right (it's not us pointing to this)