What are the ramifications of changing Armor Class to be Constitution-based instead of Dexterity-based?

It’s never made much sense to me that your Armor Class is based on your Dexterity modifier, which carries the implication that you’re harder to hit because you’re somehow nimbly moving out of the way of an attack, whereas armor is about making you harder to injure (which seems right up Constitution’s alley, particularly as inanimate objects also have an AC).

I’ve been considering implementing a rule in my games that changes AC to be calculated based on your Constitution modifier instead of your Dexterity modifier, so per the title, what would be the ramifications of this?

The only thing I can currently think of is that it’d make some classes a little less MAD and making Dexterity a little less of a golden stat; I couldn’t see it affecting Unarmored Defense, Mage Armor, a sorcerer’s Draconic Resilience, since those provide alternative ways to calculate AC already, but I’m sure there’s something I’m missing somewhere.