Nitpick - there's no double specs in 2e. Not a big deal.
But, I'm going to disagree with you that the 5e fighter leans on 2e here. Particularly when you add in things like Shield fighters granting disadvantage, and then feats granting all sorts of other effects - which, with bonus feats, is part of a fighter's schtick.
Can you make a pure DPS fighter? Sure, always could. But, 5e fighters are hardly limited to that. And, you're also fixating on levels 11+ where fighters gain their 3rd attack. For most of the game, there's functionally no difference between any of the fighter types - they ALL get two attacks. In 4e, you dealt bigger damage by tying in daily powers. 5e doesn't have that, so, let's focus on encounter stuff. BM manoeuvres and 4e encounter powers do line up pretty well, given the differences between the systems. Sure you don't get the push/pull effects to the degree you got in 4e, but, you DO still get maneuvering powers and powers which turn misses into hits, and reactive powers. Sounds a LOT like a 4e fighter and pretty much nothing like a 2e one.
I think you're fixating on the trees and not seeing the forest.