I mean, it's not like D&D has ever done a great job emulating all of Appendix N, anyway.
But, y'know, "assume everyone gets to be supernatural at higher level" (or otherwise making martials not juts martials anymore), and moving the goal posts by re-defining the genre examples inspiring D&D, both are really just denying the premise.
We won't fix the martial/caster gap by justifying it differently, and there's no need to justify fixing it, in the first place. No matter how much you want to limit martials on the grounds of Realism, there are no such grounds setting a low bar for the power of casters. Settle on martials everyone can agree on, nerf the casters down to that level. Even if that means they're just doing card tricks.