That's not what I mean by "storyless". It might be more appropriate to use terminology like "Primal Archetypes". A type of character that is deeply imbedded in shared stories. The noble knight, the devious rogue who may or may not have a heart of gold, the absent minded wizard/professor. The "great leader" is there, but they pretty much always lead from the front, they don't stand at the back telling others what to do (unless they are a villain).
Not everything in 4e was bad, but the idea that "we have to have a support character that doesn't use magic but is just as good at supporting as a magic using character" is a bad idea that arises purely out of game mechanics with no story basis. That's what people have such a hard time making one for 5e. Look at the Law cleric - designed to do the same job but "oh no, it doesn't count because it uses magic".