With regard to the whole LFQW thing...huh...mmm...hmmm....nope. Never encountered it in all my nigh-40 years of play
yeah, and George Burns smoked cigars and lived to be 100, but tobacco still causes cancer.
with ONE exception: 3.5e. That game was borked beyond all recognition unless the DM knew and owned EVERYTHING for it or had fetish for saying "No".
3.5 was the high point of caster supremacy, yes.
"A Casters true balance is measured over the course of months and years of play. Not over the course of a single combat".
Classically, the magic-user, and generally, other casters, were balanced over a whole campaign, starting weaker than non-casters for a level or few, pulling equal through the 'sweet spot,' and dominating the later game (if the campaign ever got that far). To really experience balance, you'd have to play a caster not just in a full campaign, but casters in many campaigns, including some in which your magic-user died at low level, and some that never reached the high level pay-off, at all.
I don't think that amping up the power of the martial class will help. I think the answer is narrowing the *versatility* of casters.
I think either narrowing the focus/power of casters, or increasing the power/versatility of martial classes could help. It's not like it hasn't been done with some success in many other games and even one other edition of D&D. It's just that the core branding of D&D has become associated with the feel LFQW gives, so if it's addressed at all (rather than merely complained about on-line, which remains a popular pass-time we'd be loath to give up entirely), it has to be as a set of options.
Again - your supers comparison is leading you astray. You're asking for not something small. You're asking for something that, in the context of the game, is clearly unreasonable: a complete genre overhaul of the entire game.
It's definitely not something small, it's on the same scale as wanting 3.5 levels of customization with feats & MCing & PRcs (which I also think is reasonable, BTW). And it wouldn't be a genre overhaul, so much as a genre reconciliation. Just put all classes in the same genre. Don't design non-casters as if they were in a gritty-realism low-fantasy genre and casters as if they were thinly-veiled supers with fantasy trappings ('high fantasy' doesn't even begin to cover it, LotR was high fantasy, and D&D casters leave Gandalf &co in the dust).
The only resolution is either to stop thinking about D&D as a supers game, or to stop thinking about D&D. Really.
There are two plausible resolutions: add options to bring the whole game up to the casters' 'supers' level, or to drag most of the classes down to the non-casters' 'gritty' level.
Or, I suppose, aim for something closer to S&S. You'd have to boost non-casters a bit and pull casters down some, but most of the 'balance' could come from making actually using spells extremely risky, not just inconvenient or applying lame RP restrictions or doing a few dice of damage when you flub a roll, but carry an inevitable risk of loss of the character (death or loss of control as it becomes a monster or insane and must be put down by other adventurers).