The question isn't whether or not the PC should be bound. The question is whether or not the player should be bound - and, in particular, bound to the GM as the arbiter of alignment at the table (which is the standard D&D approach).
Ah, I think this again comes down to play style.
I have the impression that your style is more storyteller type narrativist, while mine is first person narrativist and simulationist, where everything outside the player's character is in the DM's control. Nothing wrong with either approach, of course.
I think the question is if it's easier to add mechanics for how PCs are bound to their deities or remove them. As you say, having them is the standard D&D approach.