You ask for the impossible. I believe this was already attempted in 4E where each power was only slightly differentiated by flavor text from other class abilities
Your belief is mistaken. There were certainly a few powers within a given source that were virtually-duplicated between two classes, but nothing near the number of spells classes had traditionally shared outright (and do so to an even greater extent in 5e). While 4e used a smaller number of mechanics, conditions, & damage types than 3e, the many possible combinations of them, along with exception-based additions, produced thousands of unique 'powers' - which could be further cosmetically customized by changing flavor text (which may be what you're thinking of).
4e was better-balance than D&D has otherwise been, but no where near either the ideal/perfect state hypothesized for the sake of discussion by the OP, nor the degenerate state of total imbalance that you postulate. (Yes, imbalance, because meaningless cosmetic-only choices are as imbalanced as meaningless obvious-best choices make all others.)
You have to understand why powergaming is what it is. There is a certain subset of players that care for absolutely nothing but combat.
Well, OK, there is. But you can powergame other aspects of the game than just combat (cf 3.x 'Diplomancer' builds!).
Very few people care if you're powergaming social or non-combat abilities because they could care less about the outcome of non-combat events even if the DM tries his best to make them important to the campaign. They would rather not even play if the game is not focused on combat. They will find something else to do like playing a video game or watching a movie rather than engage a social encounter or non-combat encounter in D&D. I don't know what specific percentage this is, but based on my experience I would put it in the 70 to 80% range of players that prefer combat over all other aspects of the game.
That's quite another issue, and it's debateable whether the preference is innate, or driven by how poorly D&D has generally handled (and balanced PCs in) non-combat challenges.
A powergamer does not want someone else to do what he does as well as he does it. It would be unsatisfying to both powergamer 1 and powergamer 2 if they were doing the exact same damage, even if one was doing it with magic and the other with a sword.
Y'know, it occurs to me that the OPs question was personal, and you're speaking for all 'powergamers.' There's not even a definitive meaning attached to it (for instance, I consider a powergamer to be like a 'power user' in the 90s, someone who can get the most out of a system - a label denoting ability, not motivation).
That's what feeds the eqo of powergamers. They want to standout in the group. They want to be the most powerful and effective in combat. I don't think there is a good way to balance that in an RPG, especially a tabletop RPG.
Indeed, the desire to approach a game involving several other players in a way that allows only one of them to have fun with it is not amenable to balance in any sense.
They want to feel empowered in a way they can't in the real world.
You don't have to dis-empower the rest of the table to get this bit, though. The fantasy genre offers many such opportunities.
I would love D&D to finally make a game that worked past level 10 or so without so much modification.
It did, but only for a few years - and you hated it. ;P (Actually, I know it's highly debatable, but I feel like 5e can work for a bit beyond 10th... and so could 3e, unmodified, if you had a strong DM and players who exercised some consideration and restraint.)