They may have seen AMD selling their own first-party cards and anticipated AMD eventually following Nvidia’s footsteps. As for Intel, at that point they were probably seen as too much of a gamble to invest in (and probably still are, to a lesser extent).
This compares with PSUs which apparently have a massive margin.
EVGA might come back to the GPU manufacturing space with AMD eventually but Sapphire and Powercolor already fill the niche that EVGA filled for Nvidia cards (high build quality, enthusiast focused, top of the line customer support, warranty, and repairs). So it probably was just not worth picking that fight when the margins aren't really there and AMD is already often seen as "the budget option".
If AMD manages to pull a zen style recovery in the GPU segment, I would expect a decent chance of EVGA joining them as a board partner.
Sure, "unreasonable".
The first is MS' trouble with the original Xbox (https://www.gamesindustry.biz/ati-to-provide-chips-for-futur... - not a great example (20+ year old articles are hard to find) but mentions the issues MS had with Nvidia)
Then there's Apple's drama, which involved warranty claims for laptop parts that led to them being AMD only until the Arm move (https://blog.greggant.com/posts/2021/10/13/apple-vs-nvidia-w...)
Sony only went with Nvidia for the PS3, but that may be more about AMD's APU offerings than Nvidia's shortcomings.
Whether these are signs of a trend or just public anecdotes is in the eye of the beholder or kept away in boardrooms.
It’s second-hand info so take it with a grain of salt, but I read somewhere that there was a lot of friction between Apple and Nvidia because Apple likes to tweak and tailor drivers per model of Mac and generally not be wholly dependent on third parties for driver changes, but that requires driver source access which Nvidia didn’t like (even though they agreed to it for quite some time — drivers for a range of Nvidia cards shipped with OS X for many years and those were all Apple-tweaked).