I guess some people just can't imagine that something not explicitaly called magic could be magic. I don't have that problem. It's pretty easy actually.
No. My problem is that "magic" comes with HUGE baggage like:
"Oh so Fighters shoot lightning bolts out of their hindquarters now?"
"Ah, good to hear that my Fighter will be shut down by a
counterspell when doing her stuff. Just wonderful."
"But Fighters can't be magic, then there are no nonmagic classes left!"
"I wonder what hand-jive and weird Dog Latin phrases Fighters learned in order to jump really far, so strange that that is required..."
Etc., etc., etc.
It isn't that I don't think magic contains a lot. It does! Of course,
D&D 5e is kinda at fault here for continuously shifting more of the game's contents...even things that aren't supernatural at all like "shoot multiple targets"...into being specifically spells, which is just once branch of magic, but that's a digression for another topic.
It's that magic excludes many of the amazing, heroic, astounding things martials should be able to do, if our inspirations are European myth, literature, and folklore. There is no place in "magic" for "he's just such a good blacksmith, the swords he creates have souls of their own." Nor for "she can just hold her breath for three hours, no big deal." These things are impossible in real life. We are not talking about real life. This is a world where species are created by gods directly, where interbreeding between many many many different species is fully possible without any complications. Where bus-sized lizards can fly on wings that couldn't keep a hangglider aloft. Where women and men can be roasted by a fire that would instantly incinerate a warhorse, but which these heroic individuals shrug off as a Tuesday afternoon.
That is why "magic", as broad as it may be, is still too narrow.
I was starting to look at the good of 4e, but now I am starting to not like it all over again. I try to explain what I don't like and why, and I am insulted as being unimaginative.
I mean... it's literally a demonstrable thing WotC
actually did, repeatedly pretending that 4e never existed and then "inventing" 4e's way of doing it ("What about what I like to call 'passive perception?" asked Monte Cook,
literally just regurgitating 4e, even in its actual terminology, but pretending it was brand-new). And then the
several more things where they took only the most trivially superficial impression of 4e mechanics, and then actively worked against anything even remotely like what the 4e mechanic was for (Hit Dice, cantrips, subclasses, "monster builder" stuff, etc.)
Partial success! That is a great way to frame it. I actually like the idea of partial success. Along with success, critical success, and failure. Now failure sucks, but do you know what is worse? Never failing. It's (imho) boring.
Why does "partial success damage" (if that is your preferred term for the exact same mechanics...) mean "you literally never fail ever no matter what"?
What this oh-so-offensively-named mechanic does IS NOT "you just cannot fail." Instead, it pushes a tension situation (like combat) toward resolution, one way or another. I have no problem with
either PCs or NPCs having such mechanics. I think it is extremely good and healthy for a game's design to avoid encouraging "and nothing happens" results. Those bleed tension dry and turn what should be exciting and memorable moments into drudgery and bookkeeping.
A similar design concept that I think D&D needs to pick up, sooner rather than later, is "fail forward." Note that, just as the above, failure is still bad. It's still not what you want to have happen. (Edit

"Fail Forward" simply means that
failure does not grind the game to a halt. E.g. if the party just flat-out must get through a particular locked gate...they will! But whether they do so fast enough to achieve their ends, or without sacrificing something important, or without suffering a terrible setback? That's where the failure comes in for fail forward. Sure, you pick the lock--but you get through after being positively identified by
numerous bystanders, meaning your cover is blown and you'll have to lay low or skip town. Sure, you find the secret entrance--after
hours of trial-and-error frustration, at which point the cult has already killed their sacrificial captive and left the scene, so now you must figure out where they'll go next. Sure, you rescue the hostage who is the only person who knows the secret you need to learn--but they're comatose from the poison, so you still don't know what you need to know and have to solve this
new problem. Etc.
And, unrelated to the above: Does this mean you have ruled at your table that every spell which says it has reduced effects for a successful save actually has no effects at all? Because otherwise you are again saying magic is just better, magic can be an auto-win button and that's totally cool but martial things can't do that because...reasons? Assuming you did fairly take away this thing from magic that you're so vehemently opposed to, have you thus compensated Rogues and Monks for making what was a special class feature for them a generic thing?