I don't think the mage could match combat prowess of the fighter. Fighter gets better BAB and more attacks earlier. HP keep him alive longer. Plus access to better armor and weapons without having to use feats like a mage would. Sure you could play an alternate class that gets better weapons and armor like the warmage but they have a limited spell list which hampers their usefullness.
Armoring spells like Greater Mage Armor and Shield give you a huge boost to AC without armor check penalties or resticting Dex. But they have duration, can be dispelled, don't work in antimagic fields, and there are feats/abilities which can negate them. One in particular actually lets you pierce magical defenses and dispose of them in one hit. Some spells like barkskin and ironskin provide more effective HP but again can get removed.
As for weapon selection, fighter gets much better weapons. The damage and crits on simple weapons are not that great. Granted as a spellcaster with item creation feats you can probaly get a better magical weapon than the fighter in the group. But the fighter chance of hitting and criting are better. Weapon Focus and Specialization available only to the fighter make a great difference in average damage.
As for getting rid of classes, some systems do this with point buys for abilities and spells. I always liked the distinction between classes. If you try to multiclass, you can turn into a Jack-of-all-trades but you are a master of none. I always like how the mage can fill in different party roles, except healer, by wisely choosing his spells. But he can never match the prowess of the fighter, the finesse of the rogue, or the stanch support provided by the cleric.
... AND ON THE EIGHTH DAY, GOD SAID, "I NEED A DRINK."