Yup, SCAG and PHB both say that.

It's nice freedom for TT characters, but CRPGs need class/race dialogue lines that represent defined archetypes which resonate with majority of players.

If say a class dialogue line makes those players reject it, it's strayed too far from archetype. And as you said it, most paladins have a deity.

This said, paladin dialogues are tagged [Paladin of Ancients/Devotion/Oathbreaker] which seem to reference oath and class directly, and deities indirectly. I find this acceptable because [Cleric of X] should have the strongest deity dialogue lines. It also gives reason for paladin/cleric multiclass.