Paladins were based off of that, but the themes of Greek Heroes and their abilities fit the 5e paladin better than any other class, IMO. The 5e Paladin has many abilities that "Christian Paladins" didn't. Christian Paladins were basically just knights, they didn't have magic and spells, wings, and so on. To say that they did have those in Catholic History would be blasphemous.
(I'm not talking about religion, I'm discussing the root of paladins.)
Greek Heroes, on the other hand, had great strength, supernatural powers, amazing senses, and many other abilities that fit the paladin better than any other class. They can smite evil-doers, kill monsters from the "Pit" (Tartarus/Abyss), heal others, do miracles, and so on. Greek Heroes fit the 5e Paladin better than any other class, and IMHO, better than Catholic Paladins do.