I'm going to throw a shoe in here.
1. This is a fix to the Champion fighter.
2. It is not balanced against other fighter subclasses.
3. The Champion fighter must remain simple to build, and simple to play.
4. The 5 minute adventuring day is a problem for the Champion fighter.
5. Save-or-suck/lose is a problem for the Champion fighter. They have little to mitigate it.
6. Flying, invisibility, hiding, and other ways that shut-down the Champion fighter being able to attack are a problem for the Champion fighter.
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Level 3 gives you some "5 minute" day power; being able to burn HD with Second Wind.
You constantly gain more saves, until at level 15 you are proficient in all saves. This mirrors the OD&D "fighters have the best saves".
Level 7's improved Proficiency shores up your utility a bit. The jump rules get extended significantly, so you can match or exceed Olympic feats of jumping.
An additional fighting style at 10 was boring. So now you get a super-dodge with second wind (this also shores up 5 minute adventuring day power).
I'm focusing on defence rather than offence, as fighter DPR was already fine.
Level 15, we play with advantage/disadvantage on top of the existing 18-20 crit range.
Never suffering disadvantage is a really neat mechanic -- Frightened, Prone, Exhasted? Still can make attacks. This is mostly a defensive ability.
The advantage trigger is to deal with "why not just ignore the fighter". You get an alpha-strike if you win initiative, and after that the enemy has to connect in order to make you less scary. It is a taunt-less tanking mechanic.
18 was an ok ability, but it was a level 18 ability. It competes with level 9 spell access. (spellcaster cantrip scaling is automatic, and is what the 4th attack competes with).
So we get a 2nd second wind, with both shores up 5 minute adventuring days and boosts durability even more. Then we add in the ability to "sidestep" attacks and spells; this is a very tactical ability, as staying "near cover" can make the difference between shrugging off a save-or-die and death.
So now, a 10 charisma fighter has a +6 save bonus, makes saves with advantage if they have used their second wind, and can force a reroll 1x if they can shift to cover and then another time with indomitable.
Against a DC 25 effect, that is almost a 50% save chance. Against a DC 20 effect, a 73% chance to save. A DC 15, 94% chance to save (assuming nearby cover and indomitable)
Before, it was ~50% at DC 15, ~10% at DC 20+.
The only offence boost I gave the class was the level 15 "threat" ability, and really good grappling. Everything else is utility, endurance and defence.