I disliked detaching Paladins from Gods a lot until I realized it allows for religious strife within a church or amongst believers in the same god. An oath of vengeance paladin of Tyr would have quite a different view on things compared to a oath of devotion paladin of Tyr. And it might clash with the clergy of Tyr as well. However, the Paladin undoubtedly has divine power, presumably granted by Tyr. Finally I have a way as DM to portray a more complex religious belief within a single church.
However, not being able to select a deity for all characters and Paladins especially is grating on me. There are very few faithless in Forgotten Realms, and I imagince close to zero faithless Paladins. A vengeance paladin of Asmodeus or Jergal is quite different from a Ancient Paladin of Eldath. If the game can't account for the variety of the gods and faiths, it also should mechanically enforce breaking an oath it doesn't even attempt at understanding or portraying.