Ok, so the problem isn't that you want magic to be inherently better than martial/mundane, it's just that you need to rationalize it so it does not break your suspension of disbelief.
Let's see if we can agree with this:
Wizards have powers that allow them to damage several people in an area (lightnign bolt), can overcome hit points (hold monster), instantly kill a monster (finger of death), disable them (blindness), become too hard to hit (Displacement), and too hard to kill (stoneskin).
Let's see if I can build some martial movents that can be balanced toward those, without feeling "magical".
Let's suppose a power where you charge in a line, attacking with your sword everybody in your path. That's equivalent to a lightning bolt.
Let's create a power where you make an Intimidating shout, and a target cower in fear in his place.
Let's creae a power called "beheading" (or "heartseeking", to use it with arrows), that instantly kills a creature who fail saving throws, or have a certain treshold of hit dice/hit points (like Power Word to Kill)
Now let's go with a power called "gouge", that makes a creature that fails the save to be blinded.
Then let's make a "dodging stance", which makes you dodge 50% of the incoming attacks, just like Displacement does.
And now let's build a "defensive stance" which gives you DR 10, like stoneskin. As hit points aren't meat, but also stamina, will to fight, dodge, and ability to turn a big hit into a lesser hit, this damage reduction does not come from your skin being hardened (as the spell), but from you being better at dodging, parrying, and turning hits into glances.
There you go. As you don't like martial dailies, we can have two options:
1) those are at-will. Yep, the wizards will cry. But we don't care about balance, it's not a problem that a class is inferior to other, as long as there is in-world verosimilitude, and this powers are verosimile for a mundane character. The wizard will be clearly inferior in combat, but if we didn't worry about the fighter being inferior, we don't really have to worry about the wizard being inferior. Unless, of course, the problem is we secretly really want fighters being inferior, period, and everything else is just a excuse to rationalize it.
2)If 1) doesn't work, we can give the fighter a set pool of points called "fatigue" or "stamina" or "adrenaline". He can use those to activate this skills, until he is too tired to do any more. He can repeat them, to avoid "plot coupons". He, as a character, is aware of this powers being tiring, just like he is aware of his hit points. So it's not dissociative.
Would you accept this solution?