In D&D 5e, gods only really affect Clerics and Paladins mechanically. Currently in BG3, there is no correlation between your god and your cleric domain, so all mechanical aspects of your religion have been removed. But in the Forgotten Realms, it isn't just Clerics that worship. Why not allow any character to choose a religion or (for non-divine classes) to choose to have no religion? Gods, archfey, archdevils, etc and their relationships with people is a very interesting aspect of D&D. I haven't played BG3 in a long time, but when I did, I played as Light domain Cleric worshipping Selune. I got to have some interesting interactions with Shadowheart as a result. I think that's great, but why wouldn't Shadowheart try to actively convert other party members that she liked to her faith? On the other hand, getting some signs from a chosen deity would also be really rad.

But even if it is never brought up in the game, it'd still be cool to be able to define that part of your character.

Actually, Gods do not affect Clerics and Paladins mechanically. How-and-why those Classes can cast spells is flavour, not mechanism. You're free to choose that it comes from their faith in Higher Ideals with cosmic relevance, the Power Of Questing, of whatever you want. Now, sure, for Paladins and Clerics (and sometimes Rangers and Druids as well, at least it used to be the case), "Magic is granted by the Gods" is the standard explanation. It's just that the latest iteration of the game, 5th Edition, makes it a bit clearer that, hey, even if you're playing in an official DnD setting, you're free to deviate from "Paladins and Clerics must be followers of a particular God".

Other than that, I fully agree with you.

Every character should be able to choose a Deity.

With "none in particular" being the default option. If anything, it's so that people who don't want to select a Deity for their Fighter or Wizard can click "adventure forth" without their character being assigned a Deity.

This is a very frequent request. Previous discussions include
this one,
this one,
this one.
And more broadly,
this one,
this one,
this one.

I did a search before making this topic, but I guess I used the Search feature wrong or it was broken. Anyway, I'm glad it's a frequent request. I think for that reason, I can expect this to change in the release version. Thanks for the reply.

I will say one thing that isn't mentioned in these other topics is the option of conversion. I think characters should be able to convert from one religion to another, in a dialogue option at a temple or with a wandering priest. I think Clerics converting... probably would require a whole quest line, so maybe they should be forced to worship the same god from beginning to end.