Li Shenron
Legend
It would have probably been more elegant than the current rule, since armor is the only kind of proficiency in 5e that doesn't actually grant the proficiency bonus.
I don't think the balance of the game would be broken, but numbers would be adjusted in other places. For example, there are characters who are normally not proficient in any armor, what happens to them? With this sytem, they would lag behind more and more as they level up. So one option would be to grant the proficiency bonus to everyone's AC when not wearing any armor; another option would be to grant it specific features like the Mage Armor spell or the Draconic Sorcerer's natural armor, but that's a lot more work.
And then maybe all the monster's ACs might need some revision, unless it's ok to generally boost the PCs at higher levels.
I don't think the balance of the game would be broken, but numbers would be adjusted in other places. For example, there are characters who are normally not proficient in any armor, what happens to them? With this sytem, they would lag behind more and more as they level up. So one option would be to grant the proficiency bonus to everyone's AC when not wearing any armor; another option would be to grant it specific features like the Mage Armor spell or the Draconic Sorcerer's natural armor, but that's a lot more work.
And then maybe all the monster's ACs might need some revision, unless it's ok to generally boost the PCs at higher levels.