The reason why a "non-magical" Fighter has no place in High level D&D.
Wizard 20 can single-handedly take over the Earth in XXI century. Fighter 20 is a man in a tin can with a big knife. In XXI century he can fight with a motorcycle gang, unless they got a granate launcher - and some do.
Think about the power level of a wizard and a non-magical fighter. If you think about what game rules are supposed to represent, a non-magical figher is a medieval knight, perhaps better trained, but on the same level. A wizard is equivalent of something from XXX century. Guess what, medieval knights don't exactly inspire terror in modern armies. On the other hand, an egg-head from XXX century isn't very good at swinging swords - but he doesn't need to be.
You can play that game, and you will always get Twain's "A Connecticut Yankee in King Arthur's Court ", with the knights blown up left and right. It is good for a bit of laugh at the idiots who agreed to play the knights, but nothing more.
If you want non-magical fighter to be able to fight wizards, you must pull wizards down to the level of actual medieval spell-casters, as described in romances, sagas etc.
That means no more Walls of Force, Gates or Wishes. On the other hand, you get to run around with a sack over your head to cause a blizzard.
And here is a short quotation from "Yankee"
"The sun rose presently and sent its unobstructed splendors over the land, and we saw a prodigious host moving slowly toward us, with the steady drift and aligned front of a wave of the sea. Nearer and nearer it came, and more and more sublimely imposing became its aspect; yes, all England was there, apparently. Soon we could see the innumerable banners fluttering, and then the sun struck the sea of armor and set it all aflash. Yes, it was a fine sight; I hadn't ever seen anything to beat it.
At last we could make out details. All the front ranks, no telling how many acres deep, were horsemen—plumed knights in armor. Suddenly we heard the blare of trumpets; the slow walk burst into a gallop, and then—well, it was wonderful to see! Down swept that vast horse-shoe wave—it approached the sand-belt—my breath stood still; nearer, nearer—the strip of green turf beyond the yellow belt grew narrow—narrower still—became a mere ribbon in front of the horses—then disappeared under their hoofs. Great Scott! Why, the whole front of that host shot into the sky with a thunder-crash, and became a whirling tempest of rags and fragments; and along the ground lay a thick wall of smoke that hid what was left of the multitude from our sight.
Now ensued one of the dullest quarter-hours I had ever endured. We waited in a silent solitude enclosed by our circles of wire, and by a circle of heavy smoke outside of these. We couldn't see over the wall of smoke, and we couldn't see through it. But at last it began to shred away lazily, and by the end of another quarter-hour the land was clear and our curiosity was enabled to satisfy itself. No living creature was in sight! We now perceived that additions had been made to our defenses. The dynamite had dug a ditch more than a hundred feet wide, all around us, and cast up an embankment some twenty-five feet high on both borders of it. As to destruction of life, it was amazing. Moreover, it was beyond estimate. Of course, we could not count the dead, because they did not exist as individuals, but merely as homogeneous protoplasm, with alloys of iron and buttons."
On the other hand, some people want non-magical Fighter in the game-world (so eg that the wizards are rare and unique, or they want looking mostly like Middle Ages). The solution?
To replace the Warrior NPC class with the Fighter, exactly as described in SRD. This is no loss: even if in some adventure there is a statblock of a Warrior, it can be used as is, since it has no special abilities. If an adventure suggest using a Warrior of eg 2 level, a fighter can be used instead - he certainly won't prove too dangerous!
For those who like the Pathfinder Fighter, the solution is equally simple. It can be seen that the fighter class features are roughly equivalent to feats. It would be therefore easy to change Bravery, Armor Training, Weapon Training etc into feat trees, and add the following note to the Fighter NPC class:
"The Fighter NPC class can be used also for player characters. In that case, the Fighter receives a bonus feat each level, instead of each even level. Before a player takes the Fighter class, he or she should consider the fact that the Fighter is weaker than other classes at high levels."
And for those who want a high-level melee combatant who can compete with mages, there are a few archetypes available:
-Legendary Fighter - such as Cuchullain or those from Mahabharatha. He is clearly "magical", but his magic is "inborn", not "wizardry". Many, but not all of the Legendary Fighter would be Barbarians.
-Similar to the legendary fighters are various Demigods, immortal eiherjar etc.
-Magic-using Fighter - a figher who uses magic and magic items to supplement his fighting ability. He uses the "wizardry" magic and magic items. An example of such Fighter can be found eg in the Irish Story of the sons of Turenn.
Such a Fighter could be exceptionally proficient in using the magical items and technology produced by wizards. The wizards can cast spells with more proficiency, but such a character is much better in using magical items than the wizards themselves. I think this is entirely reasonable - modern pilots or soldiers are much better at flying or fighting than the engineers who create their planes or guns, and nobody thinks it strange.
-Divine or Mystic Knight - something like a Paladin, eg Galahad from the Round Table Stories.
-Fighter with Artifact Sword (or some other artifact) - A fighter who for some reason gained access to a powerful artifact or special magic, which allows him to "punch above his weight". An example would be of course the Eternal Warrior of Moorcock with his sword, or Dilvish the Damned of Zelazny with his iron horse and the city-destroying infernal spell. Of course, that sword or whatever would be a class feature, because this is what makes this character useful at high levels. This also has its origin in the Medieval Sagas. The original Black Sword was Tyrfing, the cursed sword which could kill even gods, and which was once the god of Tervingi.
- And of course, the universally hated Wuxia Warrior.
Each of those archetypes (with the exception of Wuxia warrior) fits in the "pseudo-medieval" world, since each is based on the Medieval or earlier myths and legends. Each could also be a basis for a class which could be useful up to 20 level.