Key problem: as I've argued for quite a while now, "magical" things are a very specific subset of supernatural things. "Magical" has so much baggage in D&D, it can't be the standard we use, or it 100% WILL be rejected by a ton of people. Doesn't matter if you're directly trying to do it for their benefit. Doesn't matter if you're using "magical" to mean anything that isn't "extremely plausible for an ordinary human to do". People will see or hear the word "magical" and reject it outright, because the baggage of "magic" is far too much to accept.
This design's premise is that, at least at high levels, we are going to embrace magic. That D&D is a game about magical characters doing magical things with magic, and that if you want a grittier game with lower stakes and more grounded kinds of fantasy, you're going to want to fit that in about the first 5-10 levels. Once you're slaying elder dragons and pit fiends and whatever, we're gonna assume you're doing that with magical help, and we're not going to pretend otherwise.
That may very well be a non-starter for some folks, but the reason I trotted it out there is to see if it
really was.
It seems like it has a bit of traction, more than I thought it would, so I'd wager it's an avenue with exploring. It
is a pretty big change from the assumptions of 5e, but since it relies on class features, it's not impossible to put it in the game as it is today...
Which is why I keep saying that there needs to be a space for things that are--explicitly!--not magical, but which are still beyond the limits of the mundane. That space includes things like becoming so ridiculously skilled with X thing, that your skills legitimately go beyond what should be possible in our world, but which are in that liminal space between "definitely 100% mundane" and "definitely 100% supernatural."
I think our difference is one of narrative more than one of effect, really. For me, there's too much semantic debate in the "what is magic and what isn't magic and what does that IMPLY?!" rabbit-hole. To me it resembles an argument about genre, and genre is fundamentally vibes-based and fuzzy at the edges (and endlessly debated on the internet, so here we are!).
The proposed design tests the appetite for explicit magic by turning the magic from something "fighters can do with training" to something that fighters
get via equipment that they exclusively can use (and are assured of getting). Turning the narrative to something with a bit more D&D historical cred and which raises fewer worldbuilding questions. We all grok magic items, and even
exclusive magic items (holy avengers and whatnot) and even magic items of colossal narrative power.
Are we OK with fighters doing magical things if we justify it in a way that's a little more...bald? A little less worried about semantics, and just says, yeah, it's magic (magic
items!).
I'm a little surprised at the harmony that proposal has managed to create, but excited by it!
There are hiccups...
This is another one of those "no good answer" questions. Assuming we want a fighter to be empowered by his gear to match a caster of equal level, getting them that item is as decisive. Does he just get it for leveling up? That's metagamey. Does he make his own? That's magical. Does the DM have to include it in the hoard? Then the player is slave to the whims of the DM.* You're never going to find a workable solution that doesn't alienate some part of the player base.
...but I don't think any of this is insurmountable.
When D&D moved from "wizards find and research spells" to "wizards get spells when they gain levels," the justification was just...study. Off-screen downtime. For clerics, it's even easier, since the spells are deemed to be more like "gifts" from the divine. Wisdom is just the capacity to use these gifts; level is just what the deities use to help "prove" you can be trusted with those gifts.
This is all pretty metagamey, but the game more or less accepted it.
For D&D to move from "fighters find magic gear" to "fighters get magic gear when they gain levels," the justification can be just as simple. "I was forging this in my down-time." Or, "I was grabbing magical resources from all of the magical places we've visited - wood from they Feywild and stone from that cave warped by the aberration cult." Or, "While Jozan was busy praying, I was studying this blade, and I think I've made it +1!"
Rogues can be similar. "I was honing this blade in my down-time." Or, "Guess what I nicked from that dragon's hoard?" or, "Guess I'm the favorite of the god of luck, 'cuz look what I made?"
I imagine we can do even better if we workshop it a bit, but I suspect the idea's got legs enough.
I suppose, at the end of the day, to bring fighters up, the magic items you give have to be things that allow for out of combat effects. It's not really an issue in combat - and that's largely why older versions of D&D got away with it - no one had any real abilities out of combat. Not really. The casters just didn't get enough spells, and, if you go to really old D&D, the spells just didn't exist. I mean, a Basic/Expert MU got, what, six, eight spells per level? I don't mean spell slots. I mean that there were actually only six or eight actual spells per level. So it wasn't like the MU was rewriting the game very often.
Putting magical gear into the hands of class features lets us diversify it in effect as much as we need to in order to feel like we're "sufficient." As much as I roll my eyes at the fad of "use the Warlock class design for everything!", you could see the shape of it there. Always-on abilities for things with passive effects; spend a limited resource on more powerful things that comes back on a short rest; you can take different paths as a melee or ranged character....
But, since 5e allows for a pretty broad spell list (much truncated from, say 3e, but, still pretty broad and gettin broader every year), we'd need to give fighters/rogues abilities that are just as broad. Mjollnir lets Thor fly, after all. That sort of thing. The problem, as you say, comes with limiting who can take the items. Because if the items are free to use for everyone, well, why would I give it to the fighter and not another character?
We can just lock it to class, just like spells are. Martial characters know their gear and rely on it in a way that spellcasters simply do not understand. Testing out a shape, what if we had something like...
Legendary Gear
At 3rd level, you begin to discover storied items with grand legacies who recognize you as a potential hero of destiny. Legendary gear is magical, and how you have discovered it is up to you - perhaps you found the item on one of your recent adventures, or maybe a mundane piece of equipment you have was transformed into legendary gear by a blessing or by being suddenly inhabited by a spirit. Legendary gear that you have only works for you. In anyone else's hands, the legendary gear is simply a mundane piece of equipment.
When this feature gives you a piece of legendary gear, you can select it from your class's list of legendary gear. If you are multiclassed, you can access additional lists. Each piece of legendary gear describes how it works.
A fighter's weapon might look like...
FLAME TONGUE
3rd-level fighter longsword
A warlike spirit of fire dwells in this longsword, which is eager to burn the world around it. You are able to keep it tamed and direct its fury. This magical longsword has a +1 to attack and damage rolls. When you use your Action Surge feature while wielding this longsword, it becomes engulfed in flames, and deals an extra 1d4 fire damage on a hit. The sword remains engulfed for 1 minute, or until you deactivate it (requiring no action from you).
If a paladin picks up this sword, the magic just...doesn't work. Why not? Well, they're not a Fighter who has selected this. The Paladin couldn't cast a spell the party Cleric had on their list, either. The paladin's skill with longswords isn't like the fighter's - the fighter understands this weapon and how to coax the fire from it in a way the paladin simply cannot. The iconic flaming effect relies on spending Action Surge uses, which I don't think everything should do, but gives us a way to limit per-day use that also reinforces the link to the class.
A rogue's bit of kit might look like this....
Armor of Shadows
3rd-level rogue studded leather armor
Prerequisite: Proficiency in Stealth
Armor once worn by the famous half-orc assassin Vrukush, who passed it onto his young halfling apprentice before it was lost to history. Now, you have found it.
This armor seems to grab at the darkness around you and helps you to hide in it. You can activate the magic in this armor to cast the darkness spell. You are able to see through the darkness you create with this armor. The spell cannot be used again in this way until you complete a long rest.
If the party druid equips this armor, it's just a normal suit of studded leather armor. A rogue, though...they
know leather. They trust it with their lives. The magic responds to that intimacy and trust in a way that the druid can never really duplicate. Even if the Druid was proficient in Stealth, they couldn't coax the same magic from this armor. And a Fighter? Maybe an Archer-type who would employ light armor? They still aren't as deeply connected to the powers of this. Heck, they don't even know the name of the famous assassin!
Making the powers explicitly magical (rather than debatably magical) means we can get away with a lot in terms of out-of-character moments with a little bit of "any good reason."
. Having a low grade fireball was apparently too much for non casters. 
