[Stormcrow]

Wizards in D&D grew directly out of wizards in Chainmail.

Wizards in Chainmail came from Tolkien. People wanted to try to recreate the Battle of Five Armies in miniature, and so the Fantasy Supplement was born. Gygax didn't stick closely to Tolkien, however: wizards were mostly just magical catapults (fire balls) and cannons (lightning bolts). They were then given other magical spell effects that appear in myth and literature. Chainmail wizards aren't Gandalf himself; they're just of the class of figures that are LIKE Gandalf (in Gygax's loose approximation). Gygax and friends were happy to import other stories' ideas into their wargames.

And Tolkien's wizards are of the robes and pointy hat variety. Thus, so are Chainmail's, and so are D&D's.

Why CAN'T magic-users wear armor? Because that would make them no longer match the robes and point hat style. That's it. D&D has a particular vision of what a wizard is, and it includes no armor. Oh sure, later on people demanded a better justification than that and sometimes someone would publish one, but in the end D&D wizards can't wear armor because D&D wizards DON'T wear armor.

If you think the D&D magic-user is too weak AND you don't feel any desire to maintain the robes and pointy hat image, feel free to let them wear armor. You'll make them more effective in physical combat this way.