To me, the bolded are such basic assumptions they almost don't need to be mentioned.
And that's precisely what I'm calling out. You are taking one thing as a bedrock assumption so fundamental it doesn't need to be discussed, while rejecting the other explicitly,
without justification. It's just...."well of course that's how it is, it just...is!" That, that thing right there, is a double standard in action. And most double standards end up being exactly what you described here: one thing is taken to be good/warranted/acceptable/justified/etc. at a level so fundamental it's beneath discussion, while the other is bad/unwarranted/unacceptable/unjustified/etc. explicitly, but without any explanation. It just isn't, and the previous just is, and the gap is never explained nor reconciled.
Wizards do not
deserve a handwave free pass just because we call them "Wizards". If the Fighter is being explicitly called to justify learning impressive beyond-natural techniques,
the Wizard needs to be held to the same standard. Anything less is "Well the Wizard
deserves to be better than the Fighter because that's Just How Things Are Done."
That said, I can do without Fighters having wuxia powers. That's Monk territory, and also their niche.
Then what are Fighters getting that is comparable?
Because if the system isn't giving Fighters comparable--NOT identical,
comparable--impact on the world, then you're openly admitting to "Well the Fighter just needs to be
worse than everyone else."