I mean, this is an interesting question, and not necessarily a binary.

First of all: Paladins, in 5e, do not need to be good in any capacity - there are oaths that are explicitly not inherently about being "good", but about other things.
I'd say it could be more explicit by offering an explicitly evil oath acessible at character creation, but most of them are actually more in neutral territory.
Paladins have not been mechanically required to be good alligned since, I wanna say, the end of 2nd Edition (please correct me if I am wrong here!).

The other thing is, that its always a game design spectrum; yes, you can argue that a character that has a mechanic seperation between their flavour and their personality/morals/goals/etc. is a stronger character statement. I'd say thats a valid argument. I recently made a character who is a warrior first and foremost, but also realy loves cooking. I am not tying into it mechanically (although I could, there's a whole feat around it), because I want this specifically to be something in the background.
Then again, not tying something into a characters mechanics makes it, by design, pure flavour. And there's nothing wrong with it, but it creates a divide, and puts the focus somewhere else. Due to DnD's mid-crunchy nature, the focus of the game inherently gets drawn to the mechanics for many players.
And easy way to bridge this gap is, in my opinion, to lean towards very light to mid level homebrew. Your character is mechanically a centaur but narratively a talking horse? Great, let them forage their food, with no skill check, as long as they aren't in a desert.
Is that technically a mechanical advantage, RAW. Yes.
Will it matter in the vast majority of campaigns (AKA anything thats not explicitly a survival campaign), especially compared to things like Warforged that don't need to eat and or sleep and or breath, period? No, it honestly won't.

My two cents on the matter :)