You have to be proficient with the armor in order to cast spells in it. Since mages don't get any armor proficiencies, you'd have to pick up a level in fighter, or else invest multiple feats Edit: or be a dwarf. (In the playtest, the only feat that grants heavy armor proficiency is Heavy Armor Master, which has medium armor proficiency as a prereq. If the full game has similar feats for medium and light armor, it'd cost three feats for a single-classed mage to cast in plate.)
That seems like a fair trade to me. I like the idea of wizards who adventure in robes or ordinary clothing, but I also like the idea that some wizards wear armor. The proficiency requirement ensures that both are viable options. It also means no need to have separate rules for clerics; clerics are already proficient with medium armor, so they can cast in it.
If you want an outright ban on armored arcane casting, you can always house-rule it out, as Johnny Champion's group has done. It dings fighter/mages, but the single-classed wizard won't suffer for it.