As it turns out, supernatural and mundane are different things and possess different properties. Wizards are a class powered by a kind of supernatural, and they can do things that those who aren't supernaturally powered, or even powered by a different supernatural source, can't do. If that weren't the case, then what you're asking for is for everyone to have the same tricks, more or less, with different names. That doesn't sound fun to me.
But this is mundanity in a world that is fundamentally--indeed,
radically--different from ours. Demonstrably so.
Flight works enormously differently. The laws of thermodynamics?
Fahgeddaboudit. Chemistry? Hah, funny joke, nothing like actual chemistry here. Biology? Welp, hope you're well-versed in spontaneous generation, sci-fi "almost everything hybridizes" stuff, and completely bonkers absence-of-any-explicable-origin things like dungeon monsters that apparently feed on the
extremely rare adventurers that stumble upon them.
Even at a brute superficial level, a 10th-level Fighter--whom you claim cannot possibly ever violate IRL Earth laws of physics--can just straight-up no-sale a dragon's fire breath. Hell, a 7th-level Rogue--whom, again, you claim cannot possibly ever violate IRL Earth laws of physics--can take a dragon's fire
directly to the face and experience...no damage. No negative impact whatsoever, in fact.
The thin veneer of "it works like Earth does" cracks as soon as you start investigating even small details. It's not even a convenient shorthand; it's at best a useful
lie so we can avoid getting bogged down explaining all the ways things
don't work like they do IRL, bringing them up only as needed.
Magic: Anything that is beyond the realm of physics, or biology or reality as we know it.
There, you good?
Nope. Because this is,
yet again, simply a "proof" by assertion. You have provided no evidence other than your personal assertion that it is the case. Asserting something does not make it true. You must actually SHOW that it is true. Give me a quote from a book that says "everything supernatural is magic" or the equivalent. Hell, at this point I'll take a tweet from a designer. But I sincerely doubt you'll find such a thing, because I'm quite sure it doesn't exist.
Unless and until you can show--not simply declare--that your definition is required, your argument completely falls apart.
D&D already recognizes that there can be things that are supernatural and not magic. Upthread, Rage was referenced as an example of something supernatural but nonmagical. Rogue Evasion, as I mentioned above, is another example of something blatantly supernatural--no one can "nimbly dodge" a dragon's fire
directly to their face, yet Rogues can not only do so, they suffer absolutely zero ill effects. Yet it's a thing all Rogues learn, regardless of their magical training or lack thereof. And at level 20, Rogues can literally just declare "nope, I got lucky on this roll, it's a nat 20"--and not even just once a day, they can do it once
per rest, short or long.
Where do these things fall, under your definition? They're martial characters, doing only "mundane" training, so--allegedly--they
cannot be using "magic." Yet by your own definition, these things, which would be impossible in the real world, and thus
must be "magic." We have a contradiction; abilities that simultaneously cannot be "magic" and also must be "magic."
Unless we recognize a form of supernaturalness that
isn't magic.