As to his voice quality going down, I know it's been a while since he did snake, but just watching this video I agree. Honestly, if I didn't see him, and I just heard his voice at the end, I would assume it was a different actor.
Yup. If memory serves, Kojima had been pretty publicly trying to burn that bridge since at least MGS3 and allegedly (?) tried to use that as one of the conditions for "I am done with Metal Gear Solid and will never make another" that he kept doing during that era.
I want to say that Hayter hinted at it going back to MGS2 during some of his interviews the past few years, but can't find any examples so assume that is a fever dream.