My head swims with the array of positions, suggestions, questions, examples, et al. being presented here. Not saying, necessarily any of them are bad/wrong or good/right necessarily...but I am wondering if the "do it this edition's way or that edition's way...or this edition X with that edition's Y" vs. "I prefer that edition's X with this edition's Y and, thus, that's 'better'..." is really the way to try and approach this.
Taking a step back, and a deep breath, something occurred to me...
Could it, actually, be as simple as a "spell chart" of combat maneuvers?
Not really in a 4e sense/flavor of "powers" but...well...just here me out, and understanding this is all very much figments that are kinda coming and going, mulling over as I type....but here's what I'm thinking...
[numbers are all just purely speculative/for the purposes of example. We can start a new thread for what numbers are "right/good/fun" some other time.

]
Mages/Wizards have spells. They get their various spell slots in various spell levels. The effects/damage/duration/etc. of various spells increase over time as the mage increases in level. Magic missile does more damage and gains additional missiles, Invisibility lasts longer (unless interrupted) and/or, perhaps, covers a larger radius, etc. etc.
The 1st level Mage has: 3 0lvl "cantrips" & 1 1st level spell. At 3rd level, the Mage has 4 0lvl, 2 1st lvl, 1 2nd.
Same goes for Clerics and other spellcasting classes. Now, for Non-casters...these are not "one and done" things, like a spell would be, but a number of choices that the non-caster could have at their disposal, in their repertoire.
Thieves/Rogues have their Skills/Tricks/whatever you want to call them. They have their chart and their lists of choices...broken into varying levels of difficulty.
The 1st level Thief begins play with: 2 0 lvl "Tricks" and, maybe 2 1st lvl "Skills." Say, at 3rd level, the Thief has 3 0 lvl tricks, 3 1sts lvl Skills and 1 2nd level Skill.
Something like: 0 Level tricks: Pick Pockets/Sleight of Hand, Move Silently, "Word on the Street" (or some such for gathering info). 1st level Skills incorporate: Finding/Removing Traps, Hiding in Shadows, Sneak Attack, etc. 2nd level Skills might include things like Disguise, Forgery, "Spying", "Knife Fighter" or "Grenadier", etc.
These skills and tricks have their own chances for success, effects, bonuses to attacks, whatever it is the skill does, that scale with level as the Thief increases in XP. The number of skills available, similarly go up and achieve separate "levels"...just as a Mage's spell use.
But, as stated, in the case of the non-casters these aren't one-and-done as the supernatural magical stuff is, these are skills/tricks/moves the characters know and can use as appropriate.
So, for a Fighter...I dunno, call 'em "Maneuvers" or "Stances" or even just straight out "Attacks". As the Fighter increases level, the effects, duration, area/distance, movement, bonuses to hit and/or damage all go up as the Fighter increases level.
You'd start with, say, 4 0 lvl "Stances" and 1 or 2 1st lvl "Maneuvers". Gaining the tiers would probably go up faster than spell use, but you get the idea.
ALSO, for the non-casters, the slots would be able to be repeated/taken more than once to increase your bonuses/effect/whatever it is the maneuver done. So some might have the effect that "this skill provides a +1 to hit and increases +1 every other level of the Fighter." Others could be defined as "this skill allows a +1 to all melee attacks. This skill may be repeated as the Fighter trains to a maximum bonus of +4 (i.e. take this skill 4 times/use up to 4 slots on it)"
So a 3rd level fighter with, say 4 1st level maneuvers might have "been trained to" (i.e. "Player decided to take") Shield Bash, Trip Strike, and "Power Attack" twice -so their damage bonus goes up by 2 and the hit penalty decreases by 2 instead of the +/-1 that taking Power Attack as 1 slot allows you (or, basically, double however/whatever it is Power Attack gets defined)
A different "archer" fighter-type character might have taken "Running Shot" (to be able to fire and move at the same time), "Immobilizing-shot" and "Quick Change" (to stash their bow and draw their short sword, or vice versa, without loosing an attack, just purely as an example since I have no real understanding of how rounds/time is going to work at the moment).
Again, total spit balling...and I'm sure its full of holes and "bad/wrong/unfunness" for some...but it just seemed to be, particularly for the 'Balance-meisters" out there...if non-casters and casters have a similar gradual increase of power..with a similarly limited list of options (which can them be expanded to infinity and beyond with splat books, optional addition modules, Unearthed Arcana's, Complete Fighter-guy, and the like).
For starting play, I'd say you could even get away with as few as 10 per "level" of Spells/Skills/Stances.
But yeah, that's about all I have here. Carry on.
--SD