The scenario that brought us to this part of the discussion is, as I recall it, that having considered compromise on initial presentation for one character, other players are jumping on the bandwagon. So... they kind of are a block.
So, here's a perspective problem that is rather central to the discussion.
Maybe to the GM who is unwilling to compromise, "the game" - the thing they want to run - is somehow special. But to the players... not really? In this scenario, we are still talking about compromise around character generation. Play of "the game" hasn't even begun! The players (individually, and as a group) haven't invested much, so no big loss.
In this scenario, the GM, who is apparently invested in this offering enough to reject players over its integrity, is the one who has something to lose.
GMs, and their specific visions, are not irreplaceably special.