As mentioned this is something AI could solve and I think this would be an example of an objectively good use case for it. Actors wouldn't be losing roles since no game is gonna have actors record literally billions of possible things the player could type for their name. Aside from the benefit of improving immersion it would also have potential for fun since it'd be funny to put a silly word as your name and have the characters call you that during serious moments.

This will change in the future. Look up SAG-AFTRA video game agreement.

My bet is in the future, beside usual VO work, actors will record custom libraries for their character in the game, on which AI will train their character's voice. So, you'll have much more than it is possible today.

It doesn't need to be everything or nothing. Voice acting can remain for other parts, but player names can be done by AI. I suspect it's not technically even hard to do and has more to do with what publishers/developers and voice actors can agree about. I can't really imagine voice actors being against using AI to mimic their voices for this single purposes - if not for a slippery slope argument perhaps, which might well be a legit concern.

For the SOTA models, speech synthesis has been indistinguishable to the average person from real voices for years now.

Having voice actors generate half a minute of 48 KHz samples would be enough nowadays for all purposes, let alone just saying someone's name here and there.

You probably can't do the latter locally, though, it would have to be all cloud-based.

In film/TV industry we use trained AI voices of actors as placeholders sometimes, until we can get ADR from actual actors who should be delivering those lines - not only they sound, both technically and artistically, as if they were voiced by real actors, but on not so rare occasion they sound better than actual ADR once we finally receive them.