I'm greatly convinced that the fighter need something out of combat, and that subclasses are the place for it.
But, while talking of old editions, do not forget a really powerful feature that they had and was stripped (apart from barony). They where the masters of Saving Throws. A high level fighter was really hard to put down with effect spells (and they where save or suck, so it was a really powerful feature).
Indomitable do not even began to compare because casters spells and monsters skills can target any one of the six stats. Re-rolling a DC 16+ save where you have a -1 (but even if it was a +2) is not that awesome.
Maybe something similar to 'Diamond Soul' it would not be bad as a basic class feature.
Edit: Or maybe rewrite Indomitable like a legendary save? Automatic but limited in uses?
I've heard people assert that fighters had better saving throws in OD&D and AD&D, and I seem to remember that being the case, but is it actually true? I went back and looked, and really it seems like AD&D is where the idea of the fighter being the best at saves became a "thing", but even in AD&D it wasn't something the fighter started with but gradually gained as they leveled up past a certain threshold.
Here's what I dug up...
Based on what I've read it doesn't seem to be true for OD&D, where fighters and clerics seems pretty evenly matched in terms of saving throws, and there's lots of variation according to specific saving throw (e.g. fighters start the worst at save vs. Spells, but then become the best later on).
In AD&D 1st edition, a 1st-level character had the following saving throws (success was rolling the target number or higher):
1st-level Fighter paralyze/poison/death 14 (35%) petrify/polymorph 15 (30%) rod/staff/wand 16 (25%) breath 17 (20%) spell 17 (20%) =>
avg. success 26%
1st-level Cleric paralyze/poison/death 10 (55%) petrify/polymorph 13 (40%) rod/staff/wand 14 (35%) breath 16 (25%) spell 15 (30%) =>
avg. success 37%
1st-level Magic-User paralyze/poison/death 14 (35%) petrify/polymorph 13 (40%) rod/staff/wand 11 (50%) breath 15 (30%) spell 12 (45%) =>
avg. success 40%
1st-level Thief paralyze/poison/death 13 (40%) petrify/polymorph 12 (45%) rod/staff/wand 14 (35%) breath 16 (25%) spell 15 (30%) =>
avg. success 35%
So 1st-level fighters were actually
behind other classes in terms of saving throws by -10% to -15% (-2 or -3 on a d20). What about at 17th level? Let's find out:
17th-level Fighter paralyze/poison/death 3 (90%) petrify/polymorph 4 (85%) rod/staff/wand 5 (80%) breath 4 (85%) spell 6 (75%) =>
avg. success 83%
17th-level Cleric paralyze/poison/death 4 (85%) petrify/polymorph 7 (70%) rod/staff/wand 8 (65%) breath 10 (55%) spell 9 (60%) =>
avg. success 67%
17th-level Magic-User paralyze/poison/death 10 (55%) petrify/polymorph 7 (40%) rod/staff/wand 5 (80%) breath 9 (55%) spell 6 (75%) =>
avg. success 61%
17th-level Thief paralyze/poison/death 9 (55%) petrify/polymorph 8 (65%) rod/staff/wand 6 (75%) breath 12 (45%) spell 7 (70%) =>
avg. success 62%
So fighters eventually surpass the other classes' saving throws by +15% to +20% (+3 to +4 on a d20). Looking at the chart, it seems like around 5th-6th level the AD&D 1e fighter is about tied with the other classes and just beginning to surpass their saving throws.
However, one thing to consider is that if the game kept going to 21st level, well, fighters saves already topped out at 17th level, and the other three classes got further improvements:
21st-level Fighter (same as 17th) paralyze/poison/death 3 (90%) petrify/polymorph 4 (85%) rod/staff/wand 5 (80%) breath 4 (85%) spell 6 (75%) =>
avg. success 83%
21st-level Cleric paralyze/poison/death 2 (95%) petrify/polymorph 5 (80%) rod/staff/wand 6 (75%) breath 8 (65%) spell 7 (70%) =>
avg. success 77%
21st-level Magic-User paralyze/poison/death 8 (65%) petrify/polymorph 5 (80%) rod/staff/wand 3 (90%) breath 7 (70%) spell 4 (85%) =>
avg. success 78%
21st-level Thief paralyze/poison/death 8 (65%) petrify/polymorph 7 (70%) rod/staff/wand 4 (85%) breath 11 (50%) spell 5 (80%) =>
avg. success 70%
Here we see the fighter's advantage diminish to +5% (+1 on a d20), or +13% in the case of thieves (+2 or +3 on a d20).
What this demonstrates is that the AD&D 1e fighter didn't start as having the best saves (quite the contrary!), but by maybe 7th level gained an edge over other classes in their saves, and the edge grew until the epic tier of play when it diminished to just a slight advantage.