[just another ref]

So we have the flexibility to grant a time-out either instantly, (even if the whistle is later) or not at all, depending on the circumstances, even though the requests that were made were identical on two plays. Is there another play where an official must use judgment to decide what a team might want?

Another angle: You hear team A's coach say "I want a time-out after this free throw." But A1 stops listening after "I want a time-out......" and asks for the time-out NOW. You have to call one there, don't you?