Would allowing Wizards to use Wisdom for AC be unbalanced?

I find myself frustrated that Wizards have high incentive to invest in Dexterity and Constitution so that the aren’t quite so squishy whereas they have little incentive to increase Wisdom except to help their Wisdom saves. Wisdom, however, seems much more in line with the common imaginings of a Wizard than Dexterity.

I am considering house-ruling that wizards can choose to add their Wisdom modifier to their AC instead of Dexterity but I want to check whether that would be balanced.

A relevant aspect to this change is that wizards have Wisdom Saving throw proficiency so this would allow them to be really good at Wisdom Saving throws more easily. On the other hand Dexterity saving throws are also quite common so giving up points in Dex also has a high cost even without AC.