Ancalagon
Dusty Dragon
If you could make a character 3x as good at combat by sacrificing social and exploration then that would theoretically work fine, it's just the fighter at best is slightly better than some other classes at combat (and he's arguably worse than most of the naturally charismatic classes).
I would say that I feel that the 5e fighter has better "out of combat support" than many prior editions because of the backgrounds. A fighter can be a sort of backup ranger or rogue for example. Some of the subclasses also help.
But it's still a sparce kit compared to some other classes. And that's why the ranger (well, phb ranger at least) or the monk have gotten flack for being weak in combat - if they were as good as a fighter, why would you ever play a fighter?!?