Here's what get's me. I agree that, with the fighting styles, the level 5-10 GWF and TWF fighters are balanced OK. But from 1-4 the TWF is considerably better, and from 11+ the GWF is better. So you could say, fix 11+ separately, and you don't care about 1-4 because it's over quickly.
As for other classes: paladins, war/tempest clerics, valor bards and barbarians don't get the TWF style, which means TWF is no good at all past level 5. Rogues don't get TWF style, but want it so bad they are kind of handicapped if they don't dip into fighter for it. Monks can't really use TWF at all, which means they are handicapped if they don't use a staff or spear until their martial arts damage gets good enough. Rangers I think probably work the best, since they spend the most time in the configuration where TWF is reasonably balanced.
That's why I think a more fundamental fix is better than a class-specific tweak.
So, now to be clear, to you the problem with TWF is how bad it us for the non-fighter classes- the ones with only one or two attacks per attack action?
Interesting, often it is portrayed as problematic when compared to the three or four attacks fighter.
To my way of thinking, for rogue, psladin and the others who get yo add in a big extra DMG on z hit or less but noticable extra dsmage on every hit the extra attack free bonus action thing is enough of a benefit especially once you add in the other bonus factors you get for free in many cases (SAD with dex, thrown for some, concealability, etc).
As for not wanting class specific "fixes" - since TWF (action, not style) is free to all but every class has differences in how they can impact damage vs number of hits, I myself cannot see anyway for a global change to not be class specific and have a hope of doing anything other than shuffling around what the top best option is based on whatever white room spread sheet one uses.
For my money, if you want homogeneous output, you need more homogeneous system. They could have done that, they chose to have actual differences and meaningful choices.
One "simple option " - change the 2dx two-hznded weapons to 1d... so instead of 2d6 the great sword does 1d12 (more sames). Then have shortsword snd dagge be d6+d4 on a hit. Apply ability bonus once, period. Apply one weapon's magic period. Treat it as one hit period. Now the only difference at the core is the roll of the dice (oh and one can be thrown, one can be easily concealed but that doesnt vount in white rooms.)
But, my bet us that eont be enough for those wanting to get both core dsmage yo match and have fighting with two weapons be the more reliable too.
But