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.