I guess ultimately, it comes down to "what do you want the Fighter to do."
For some, it seems to be "no frills weapon user who can have a strong AC, great hit points, passive abilities that are always available, with few decision points".
And the class as written in the 5e PHB accomplishes all of this.
I can't say specifically what others want, but here's the kind of things I'd want the Fighter to have (one or more):
*Tactical abilities. I'm not talking about the Battlemaster here. The Fighter should be able to work with their allies to use teamwork to efficiently deal with threats. More like the 3e Marshal than the 4e Warlord; the Fighter should have some ability to improve the tactics of their allies. Bonuses for flanking, or staying in close formation, or covering for the retreat of allies, etc..
I mean, the Wolf Totem Barbarian can grant allies advantage on attacks, but the Fighter can't? Seriously.
*Leadership abilities. Closely related, the Fighter should be a general, able to lead people into battle against overwhelming odds. A Fighter in charge of a platoon should be a force multiplier. But also, the Fighter should be the one people look to when they need a leader. This can be reflected in a bonus to social rolls, or saves against fear, or both.
*Weapon Mastery. If the Fighter is the master of weapons, then they should have abilities to let them quickly switch between weapons in combat, and to actually justify doing so! Currently the Fighter can be good at using a broad category of weapons, such as two handed weapons, two one handed weapons, a single one handed weapon, thrown weapons, or ranged weapons.
But there are times when one needs a spear, lance, mace, or sword, and there's almost no reason for a Fighter to just carry around the best weapon for a job. If a Fighter has a +1 hammer and a sword, he uses the hammer save for some odd corner cases.
And I'm not talking about specializing in a single weapon, that requires Feats, and thus, anyone can do that. The Fighter should be able to leverage their mastery of all weapons, to really drive the point home that they are the masters of war.
*Increased resilience. This used to be the hat of the Fighter and his Warrior cousins. Over time, this guy would prove to be very hard to do just about anything to, increasingly able to shrug off a wide variety of strange attacks and effects. Today, he's reduced to being good at shrugging off being pushed around, knocked prone, poisoned, diseased, or other esoteric threats to his body.
Outside of that, his resilience to area attacks and mental assault is based on his ability scores only, and over time, that is outweighed by the benefit of proficiency in a save. Indomitable doesn't cut it, as rerolling a poor save is pretty much a Hail Mary play. Sure, it doubles your chances, but that chance can still be 0% at high levels.
*Increased narrative agency. This is the hardest to figure out, but consider the party at the gates of Khazad-dum. The Rogue might try to pick the lock. The Cleric can call up on divine intervention. The Wizard can use knock or dimension door, or even bypass going through the Mines of Moria via fly or teleportation. The Fighter can...knock the door down through brute strength (maybe) or try to climb over the mountain.
Some people say this is the moment when it's ok to have the Fighter sit down and let other people do their things- but when does the Fighter get to tell everyone else to sit down and let them do theirs? It's surely not in combat, since everyone has a more or less equal role there.
*A good reason for casters to think "hey, let's use magic to buff this guy". In 3e, because of their fighting prowess, the Fighter was one of my go to targets for enlarge, aid, bull's strength, cat's grace, haste, fly, heroism, blur, displacement, blink, greater magic weapon, and the like.
Now, as previously mentioned, even if I can justify using such spells on the Fighter (if I even can, some of these spells are greatly changed), I might have a much more effective option instead.
What if the Fighter could concentrate on a beneficial spell that targets them instead of the caster? Seems pretty good...