so many good answers here
lots of good ideas. I concur with Dassul, above, that there should be mechanical reasons why wizards, through opportunity costs, would not willingly bother wearing plate or even chain. Leather I don't see the problem with. If they multiclass or spend the feats for armor (if they can get rid of armor feats entirely, that would be ultimate...not require VERY tricky balance to push people subtly or less-so towards classic archetypes due to their optimality for their role)
An optimal wizard should be in robes, because maybe his spellbook on his back is heavy enough, and they need Con to cast spells of a certain spell level. If they need strength and dex too, things get tricky. My AD&D evoker had str 10, dex 15, con 16 (required), int 17, and cha 13. We made checks in every single stat (well, except str). There would be no way to wear anything more than leather.
Gish characters should wear armor, because it makes sense if you are on the front lines to wear armor. If you are a pure wizard, you should avoid spending feats on chain and plate because those feats are MUCH better spent on other things. Leather should be recommended to wizards, as in 4e.
4e's system sucks because they allowed Int to contribute to AC, to be "fair" i.e. awww, no more squishy smart guy who can't lift a spoon or dodge a charging granny. No, no, no. If you got the Str to wear armor, you should be able to wear it.
HOWEVER, I don't agree that carrying weight / encumbrance accurately reflects battle stamina drain from wearing armor. Wizards are just not trained to fight in melee, it's exausting, you are afraid, shaking, you lose energy like mad. I'm serious. Try boxing THREE rounds against someone who's trained at it, if you even THINK for one second you are able to do that wearing leather armor, or chain, or plate, without an insane amount of training, while still pulling off complex spells requiring concentration and mental focus, ahhhh...no.
Seriously, I did kickboxing for a few years and it's insane how quickly you are drained of every ounce of strength you have. And that's not a life-threatening situation (though it certainly feels like it). Without training, against someone who has some, in full-contact or even sport-contact type sports like boxing, you are DOOMED.
So someone trying to fight without a decent strength and con in armor, is going to have disadvantage on all their attacks. If you meet the pre-requ. and have the training, go ahead. But just how many wizards do you think have good strength, good con, AND good int? Dex is a far more optimal way to boost your AC, and instead of spending one or two feats to acquire proficiency, you'd be better off taking other defensive fears or themes or spells. A gish or multiclass fighter/mage should be viable, and I see a theme could bypass disadvantage in heavy armor.
fighting is risky, life-threatening, and distracting. Fighting and casting in armor, dodging blows, in melee...should give disadvantage. That's a VERY good reason why wizards wouldn't bother. Make it a natural, emergent extension of the rules, instead of kludgy added on exceptions for certain classes.
A cost of three feats, 15 str, 13 con, should be enough to keep wizards out of plate. and if multiclassed into fighter for the feats, and you got the stats...why not. Maybe add a theme that allows you to bypass the disadvantage to casting spells (even WITH proficiency) in heavy armor.
Maybe the "armored arcane caster" theme starts you off with removing disadvantage at level 1 in light armor, at level 5 in medium, and level 9 heavy armor. A cleric with medium armor theme could do the same but one step faster, and be in plate by level 5 instead.
The opportunity cost of not taking a wizard blasty theme should be enough to keep most wizards in their robes.