The biggest problem with 5e as a whole is they setup the concept to the 3 pillars of xp (exploration, social interaction, combat) and then didn't figure out how this applies to every single class or even a proper mechanic to cover 2 of the three pillars.
even if we had pull a 4e and revise from the ground up, it would solve a ton of problems.
the fighter in particular is a problematic class from a conceptual model.
they fight...now what do they do outside of combat?
in 2e, they were powerful, but boring.
in 3e, they were given kewl abilities that were actually traps because of how many cookisms were dumped into the game.
in 4e, we build a fighter that could actually fight, but was compared unfavourably as a wizard because of design mechanics.
I honestly think changing the fighter and making it based on the Knight, Mercenary Fighter, and Soldier as archetypes which gives you an idea of what the niche is.
The Knight would include marking (like the knights challenge from 3.5 phb2 ), and outside skills like heraldry, social etiquette, and horses, falconry as well as other rudamentary skills befitting a long mentorship. If people are still terrified of the Warlord class being in 5e, this would be the closest to being one.
The Mercenary Fighter would be based on the champion and also be the exotic weapons master. He'd be the type that would pull out the spiked chains, or other wacky weapons because it's how they achieve infamy. they would also be the closest to a fighter/rogue without being one. If you really want to build a bar room brawler, this is also the one of choice and gets bonuses by being a thug.
The Soldier would give synergy bonuses to teamwork actions. They also would be the only of the fighter archetypes to get a MOS that would determine their training (Archer, Polearm Specialist, Shield Bearer, Skirmisher), that gives skill set to be used outside of combat. They also went to boot camp and learned a range of rudamentary skills to help out around the camp site and to quickly evaluate targets. This can also be the one that gets combat manoeuvres.
I'd be okay with throwing in the Eldritch Knight as well, but using this base you have a concept stuck in your head and it makes it easier to figure out what they'd be good at.
and it's also easier to figure out what they'd do outside of combat.
edit: one last thing. If the archtypes don't give you an "agony of choice" feel when trying to decide which to pick, you've failed as a game designer.