That final idea of yours is almost exactly what these drones would be, at first. Except they would be expected to hover around the ship, and be able to come back if they survive.
Which kinda negates most of the purpose of the missiles in the first place, because it means they need to be a lot bigger and more expensive and have more fuel.
Another, related but more exotic possibility, is taken straight out of Battletech. FTL drive. Ships could be cheap as heck but for the interstellar drive system they carry, which, for whichever reason (economy of scale perhaps, again) can't be fitted to small ships. Whether by dint of using hard-to-process exotic matter, or having production costs way above mere "construction" costs, FTL systems could be immensely important - allowing their use as a sort of self-hostage. "Destroy this ship and you're taking its FTL drive with it", in essence, making the combat again focused on disabling and capture rather than destruction of the enemy.
Well, in that case the FTL drive is more or less the most valuable part of the ship. Strategy? Determine where the FTL drive is and destroy everywhere else until you've knocked enough holes in the hull that they surrender or die.
I could maybe see fighters here, but mostly used as scouts with some kind of space-warping or whatever stealth technology exists alongside FTL, confirming the location of the FTL drive, rather than actually...fighting.
A rather more extremely idealistic option is simply that both sides abhor incurring unnecessary loss of life in their wars...
Thanks, I needed a laugh.
You seem fully aware of why this is unlikely, though, so I won't go into it.
Ha ha. Um, first off what kind of non-ship-destroying weapons are melting large sections of hull?!? Second off, molten metal is also magnetic, and if it was molten enough to slip off you'd have problems of big holes appearing in the ship because you basically jellied a big section of hull, and since it's big and loose enough to impede a magnatank rolling across it, it's by far big enough to blow outwards under the pressure of air inside and cause major problems for people in the ship. Forget fighters, that laser is the big weapon.
Anyways, the idea that fast-moving turrets are going to be flying off the hull...not happening with smart design, and if it is for some reason you just have competition between railturrets and magnatanks. It's not enough of an issue for people to waste the resources and such on fighters.
I was thinking more in terms of heat deformation, not loss of magnetic capacity. A pulsed laser will crater the surface, creating a mighty speedbump for any wheels (roller spheres, more likely) fit for rapid movement and change of direction. Or do you propose magnetically propelled maglev hovertanks? They'll lose all hope of magnetic attachment the moment they overheat due to induction forces. Space is hot. Not to mention they won't be able to draw power from the ship readily, making them no different from fighters - and with a much more limited and finicky propulsion system to boot.
I was imagining more like a tank with magnetic treads. I didn't give the matter much thought at any point, but it seems like the surface area of the treads would let them stick to any crater small enough for the slope to risk drifting away.
And you know what the propulsion has that the fighters' propulsion system doesn't? A way to avoid violating Newton's Third Law of Motion without carrying most of its weight in fuel. Or not maneuvering much.
Don't try to look for the perfect weapon--there isn't one.
Hence "evolution of weapons". 
If your complaint is that magnatanks have issues...well, they do. But let's look at your analogy, eh?
Evolution, despite what I really hope you don't think, does not create an organism that is genuinely better than previous species; it merely comes up with a set of trade-offs better-suited for this generation than a thousand generations ago. Similarly here. If you're trying to find "the perfect weapon" or "the perfect organism," you're going to either need to go to fiction or else find your favorite weapon/organism and figure out how to spin its flaws as strengths.
Simply put, you can't claim a weapon is terrible because it has a few flaws. You have to compare it to the other possible weapons and such, see which has more strengths and fewer flaws.
Well, I'd be glad to do that if I had time to think this through and a better handle on the starting conditions. Sociopolitical/Economic issues are implied but not stated. Why are they fighting a war? How much resources do they have? And past that, what "tech level" are we talking about?
...Did I mention that I'll probably overthink it?
Hmm. Actually, I'd be happy to discuss that sort of thing. I like worldbuilding.
We'll need to find a time and a place to do that.
You still have limited fuel, which is kind of a major issue. And how the heck are you going to be maneuvering without sending mass in the opposite direction? Isn't that a violation of Newton's Third Law of Motion?
And, um, are you saying that fighters wouldn't need to be repaired? Because that implies that they would keep getting destroyed.
Yep. They can't evade forever - one way or another they are going to get hit. And with them being not much more than a gun, a fuel tank, and an engine, the moment they are hit they are gone, simple as that. Unless extreme-rapid-fire scattershot pulse lasers are made, I guess, to just chip away at them with lucky hits.
You left out the cockpit and the life support.
And limited fuel is less of an issue when fuel on the ship is plentiful, engines are efficient, and the ship itself acts as a shield when the fighter's on pit stop.
So, the fighters are going to be sticking right next to the ship and sniping rather than engaging in techniques anything like what people think of when people say "fighter"?
And the "ultimate" (at some point in time) solution is to make more ships, small and fragile enough that they'll be destroyed by any good hit?
The "ultimate" solution is to make ships small and cheap enough to allow to destroy them with impunity, I guess. I don't know how to take that hypothetical war beyond turret fighters without starting to break the underlying paradigm of big ships being nominally safe from casual destruction.
Well...I dunno what to say there.
Also, remember that hangars pose both a significant resource cost, and a big weak point in your ship.
Hangars, small ones, I see as existing almost regardless of ship type. In absence of teleporters, you want to have a way to send someone over to somewhere that doesn't have a standardized docking port in your ship's size, and you have to have a shuttle or two - and leaving them hanging in the open on the outside of the hull is just asking for them to get accidentally blown off.
Well, yes, but a shuttle or two requires much less space and such than a bunch of fighters. And reserve fuel and such.