Been pondering this one, and I'm not one to play fighters typically, and we don't tend to play beyond 11th / 12th level to see where problems really arise, but when I think of a good fighter, I'm thinking someone who is fast /instinctive and dangerous in combat, able to take on multiple opponents (thinking of many of the fighters from the Malazan series here really).
While Extra Attack does get better over time, and action surge allows for another set of attacks, I don't think it quite captures it all.
I'm thinking something like at a certain level, a fighter starts getting their proficiency bonus added to initiative, to reflect that they will tend to react faster than most.
I also think after a certain level, every time a foe misses the fighter in combat, that foe takes proficiency bonus damage, to reflect the skill / deadliness of fighter, able to riposte / parry / take advantage of flaws in opponents attacks.
I would like some sort of automatic cleave thing in practice as well, to help give something equivalent to AOE attacks that casters get, as it appears that everything is balanced against single target damage, and so to a degree AOE gets bonus damage if multiple opponents, and would be good for fighter to get something akin to that, able to damage multiple opponents at same time, ignoring extra attack - though would need to be in such a way that it doesn't become a Bag of Rats style situation.
Outside of combat, I'm thinking sort of two paths that a fighter can choose from, and not sure how well this would go with subclass choices, where this could be encroaching on, but thinking sort of:
1: - the athletic sort of path, with a bonus (not sure what) to strength and dex based skills, especially athletics / acrobatics, to represent that a good fighter is good at that sort of thing (potentially need same for Barbarian as well) - and is where I start looking at the people who can do wall running, so perhaps 10' climb movement sort of thing to represent freedom of movement / ability to run up / off walls to get more manoeuvrability
2. - the charismatic / leadership path, with a bonus to charisma based skills, especially persuasion / intimidation (intimidating presence sort of thing). I don't see that this would cause an issue for other charisma characters, but wanting to show that a certain type of fighter could be as good as a Bard or Sorcerer at certain 'social' skills outside of magic effects at least.
My rough thoughts / 2 cents
