Question: If you're sacrificing one level of wizard (not just spellcasting--remember that you're also delaying access to your specialty benefits!) for a bonus to AC, how big should the bonus be?
Right now, a wizard with Dex 14 and mage armor has AC 15, while a wizard in plate with a shield and the Defense fighting style has AC 21.
Of course, nobody will be able to afford plate for a few levels, and in the long run it is entirely feasible for a mage to boost Dex to compensate. The best starting armor, either medium or heavy, is going to be AC 16.
The real problem is that there's zero reason for a mage, upon gaining proficiency with shields, to ever
not use a shield - it only takes one hand to use your focus. Shields give a huge boost, under Bounded Accuracy, because there's supposed to be some sort of trade-off, but you're not losing anything here. Then of course, there's also no reason to
not take the +1 AC fighting style, since you probably won't be making weapon attacks anyway; again, it's an obvious choice with no trade-off involved. The third problem is that
one level of mage is only a hindrance if it's an
odd level, which makes it really hard to balance against any particular amount of AC.
(It's also weird and counter-intuitive, but it's possibly even more beneficial to add two levels of paladin instead of one level of fighter. Because of the crazy multi-class rules, it's the same hit to your effective caster level, but you get to add
cure wounds to your spell list. )