It felt like one of the arguments was that the fighters either needed to be able to push themselves more or have magic items
I prefer this option as it reflects the more "action-hero" feel I like to see, especially in higher level fighters. Now, features like Second Wind and Action Surge
do represent this. I can recover from damage and I can do more if I need to. So, I see them as perfect for tiers 1 and into tier 2, the problem as others have pointed out is fighters have no new features after level 9 when they get Indomitable.
If we look at the features classes gained at 9th level and after. I bolded the features I consider "new"
Barbarian:
Relentless Rage, Brutal Critical (1,2, and 3 die)
Persistent Rage,
Indominable Might,
Primal Champion
Bard: Song of Rest (d8, d10, d12), Bardic Inspiration (d10, d12), Magical Secrets (3 times), Superior Inspiration,
plus spell levels 5 - 9.
Cleric:
Divine Intervention, Destroy Undead (CR 2, 3, 4) Channel Divinity (3/rest), Divine Intervention improvement,
plus spell level 5 - 9.
Druid:
Timeless Body,
Beast Spells, Archdruid,
plus spell levels 5 - 9.
Fighter:
Indomitable (1, 2, and 3 uses), Extra Attack (2 and 3), ASI (14th), Action Surge (2 uses)
Monk: Unarmored Movement improvement,
Purity of Body,
Tongue of the Sun and Moon,
Diamond Soul,
Timeless Body,
Empty Body, Perfect Self
Paladin:
Aura of Courage, Improved Divine Smite,
Cleansing Touch, Aura improvements,
plus spell levels 3 - 5.
Ranger: Natural Explorer improvement,
Hide in Plain Sight, Favored Enemy improvement,
Vanish,
Feral Senses, Foe Slayer,
plus spell levels 3 - 5.
Rogue: ASI (10th),
Reliable Talent,
Blindsense,
Slippery Mind,
Elusive,
Stroke of Luck
Sorcerer: Metamagic (twice), Sorcerous Restoration,
plus spell levels 5 - 9.
Warlock:
Mystic Arcanum (6th - 9th levels), Eldritch Master,
plus spell level 5.
Wizard:
Spell Master,
Signature Spell,
plus spell levels 5 - 9.
While many full casters are light on new features as well, they are all getting spells of 5th level and higher, which for those classes pretty much
is their feature.
If you look at just the non-full casters:
Barbarian:
Relentless Rage, Brutal Critical (1,2, and 3 die)
Persistent Rage,
Indominable Might,
Primal Champion
Fighter:
Indomitable (1, 2, and 3 uses), Extra Attack (2 and 3), ASI (14th), Action Surge (2 uses)
Monk: Unarmored Movement improvement,
Purity of Body,
Tongue of the Sun and Moon,
Diamond Soul,
Timeless Body,
Empty Body,
Perfect Self
Paladin:
Aura of Courage, Improved Divine Smite,
Cleansing Touch, Aura improvements,
plus spell levels 3 - 5.
Ranger: Natural Explorer improvement,
Hide in Plain Sight, Favored Enemy improvement,
Vanish,
Feral Senses, Foe Slayer,
plus spell levels 3 - 5.
Rogue: ASI (10th),
Reliable Talent,
Blindsense,
Slippery Mind,
Elusive,
Stroke of Luck
The fighter is the only one with a single new feature at level 9 and later. Certainly, Extra Attack 2 and 3 are very nice, and a second use of Action Surge also helps with combat (and sometimes with exploration probably), they lack the guaranteed things like Indomitable Might or Reliable Talent, and they lack all the mystical/semi-magic of most of the other features.
I think there should be a few new features to give fighters in tiers 3 and 4 that would help alleviate the issue.
EDIT: Really, this is just sad, because fighters core features are:
Fighting Style (one)
Second Wind (never more than once)
Action Surge (2nd and 17!)
Extra Attack (5, 11, 20th)
Indomitable (9th, 13th, 17th)
This has me thinking. Would you be ok getting rid of Extra Attack 2 and 3, and the bonus feats at 6th and 14th, for more uses of second wind, action surge, baking in more fighting styles, some Champion features, and the BM maneuvers?
I think you could make a much more interesting and fun fighter, without really getting too crazy on the power level.