I don't think a fighter should be anything. The existence of the class seems of questionable value to me, because while fighters need abilities to be useful, balanced and interesting, whatever abilities you give them will always cause them to break from somebody's conception of "fighter." The issue is, in essence, that fighter is too broad of a concept. Better to have a variety of class options, each with a clear set of mechanical concepts in play, and avoid calling any of them "fighter."

Now, what should a wizard be? That seems like a contingent question to me. My first instinct is that the answer is pretty much the same the reason wizards have to be too powerful is the same as the reason why fighters have to suck. Both concepts cover too much territory, save that one covers it by exclusion and the other by inclusion. Both need to be broken up into smaller, better-contained units with a clearer scope.