All you'd need to do to accomodate paladins of specific gods is to allow them access to certain dialogue choices and reactions based on their god. It's not demanding much more than would be demanded from a cleric.
Speaking about 5e as a whole, my opinion has long been that they decoupled paladins from explicit religions because they felt it went without saying. They understood that 90% of players would still give their paladin a religion because they understood that it's just how it goes that players give all their characters patron gods as part of character creation. They simply changed this up to allow for a bit more openness for those who wanted to play edge cases and provide some inspiration to stoke those more unique ideas. the problem with BG3 is that they don't allow anyone other than clerics to choose gods. (which by the way is something that Wrath of the Righteous managed to do without issue, including bits of reactivity all through the game depending on what god or religion you chose)
But the issue we have with not being able to pick is that our deity is important for RP purposes. If we get to a point where our deity or their rival is important then not being able to bring it up is as off putting as clerics not being able to bring it up
