Snake was physically old in MGS4, too, and he was still David Hayter.
Big Big Boss looks and sounds like a different person as he gets older. Hence the new voice actor as his face starts to resemble his elderly self more in The Phantom Pain.
Yes, that is likely. As I mentioned, I don't think the decision to not use Hayter (if true and not a Kojima stunt as you never know) would be for a story purpose, like Big Boss' voice changing as he got older. I don't think that they would arbitrarily decide against Hayter as he's established in the universe.
Kojima could be making the switch with an eventual MG1 remake in mind.