Well that isn’t a genuine representation of what people who disagree with you have said.
What we have said is that 4e fighters could be supernatural, but weren’t necessarily so.
In 5e, the existence of the Eldritch Knight doesn’t make Champion fighters supernatural, does it? Of course not.
Nor is my fighter in 4e supernatural just because he could have had powers that could be interpreted as supernatural.
(Also the powers you were referring to almost all use auras or other effects to more fully model the “many attacks and defense and counters in a given turn, modeled by a single action” nature of D&D combat, so no, they weren’t in any way supernatural, you just didn’t like the way they modeled the same exact thing modeled by making several attacks in a turn)