AnotherGuy
Hero
I agree with you that the fundamental issue for change (in order to realise this ideal to create the mundane and supernatural paths) lies first, with nerfing magic. Whether it is the combat or not, I'm not sure, but magic overall certainly needs to be reined in. The inherent magical power within the game is IMO too high.The problem is that even if we decide the fighter is King of Combat, we haven't fixed the fundamental issue.
Remove every attack spell from the PHB, fire bolt to meteor swarm. Wizards cannot do a point of damage without pulling out a crossbow. We have made the fighter the best in combat. Has parity been achieved? Not really. The wizard sits on his hands every time initiative is rolled and the fighter shines, then combat ends and the fighter sits on his hands while the wizard shines. You give each a time to shine but never the same time. That leads to the "wake me when it's time to roll dice" downtime that kills enthusiasm.
So you end up with one of two scenarios. You have to nerf magic to such a degree that the wizard is second in combat, but also only slightly ahead in noncombat. Or you have to buff martials so that they can play with similar toys that the wizard gets. Flight. Instant movement. Divination. Etc. Essentially, the wizard needs to be dragged several levels worth of power down to be closer to mundane OR the fighter needs to be able to break reality like a wizard. And all the grit and training in the world isn't going to help when the demon lord causes a cave in and the wizard teleports and the fighter can't.
EDIT: Just to state this is mostly a me-preference. I do not know if this preference is shared at large.