I dont really think Doctor Strange needs to exist until very late levels, and I 100% believe Magic Items need to be assumed at such a point, AND I believe Fighters need to be better delivery systems for those items, than non-mundane Classes.
This! This is how I would square the circle, if I were a game designer. Which I am not, and for good reason, but - okay, this is assuming an "ideal" fighter, who contributes as well as anyone else at "hit it until it dies" but still needs help in the other pillars and general versatility. I'd give them access to clearly supernatural abilities, but I'd make them need magic items to use them.
A high-level fighter with a Flame Tongue can melt a glacier.
A high-level fighter with a Frost Brand can make a volcano dormant.
A high-level fighter with Boots of Striding and Springing can kill three men without seeming to get up from his chair.
Nobody else can do this, for the same reason that nobody else can create a Forcecage by snorting powdered diamond. They don't know how to, and the techniques are too complicated and grueling to just walk a novice through.
Does this make the fighter, himself, magical? Not any more than a fighter pilot or a concert pianist. The potential is in the item. 99.9% of the population doesn't know how to bring it out.
Does this make the fighter more reliant on gear than other classes? Yes. But if your fighter uses anything but their bare hands and feet, you are already accepting this. I'd even argue that this is baked into the fighter class: their biggest defining feature is the ability to use every weapon and every piece of armor. By their core design, more than any other class, the fighter is a
tool user. And the better the tool, the better the fighter should be at using it.
Ideally, this wouldn't increase the fighter's direct in-combat ability by much, if at all. Like a wizard with expensive spell components, not having the fancy stuff doesn't significantly handicap them, it just takes a few of their options away.