That is true, paladins overlaps too much with fighter/cleric, but i still believe they can somewhat coexist, like sorcerers and mages/bards, is just that it would require a very radical change to all paladins, something that makes them different.
we need to ask 3 questions.
what is a fighter, what is a paladin and what is a fighter/cleric.
my answer is..
A fighter is someone dedicated to martial arts, he isnt religious, he doesnt use magic, so he need to be the best at fighting with what he have, a high level fighter can be considered a "genius".
A fighter/cleric is someone who has sacrificed part of their daily dedication to a god to learn to be a better melee warrior, he should have less divine magic than a pure cleric and should never have the same martial prowess of a pure fighter.
Then there is the main issue, the paladin.
Perhaps he should be like a fighter, but not a genius, instead he is someone so devoted to an oath that he is blessed by a specific divine even without praying, the paladin's martial prowess should be stronger than a fighter/cleric, but weaker than a pure fighter, his kit should have self buff spells to represent his deity giving him aid, but also, aura like abilities to represent the inspiration he is to his party or the fear he causes to his enemies(evil paladins).
Anyway, I know it's a little late, but I just wanted to give my opinion on the matter.