Wouldn't wearing a bunch of armor sort of kill any attempt to blend in and be stealthy? Remember AC1, Altair never got to upgrade his armor. In AC2 Ezio did get to upgrade his, but he lived in a time period when it wasn't out of the ordinary for a man of means to wear some form of armor in his day to day life.
Now, look at AC3. It's set in the 1770s(mostly) and people just didn't wear armor. Wearing armor would make him stick out in the crowd pretty badly. And, why do you need armor anyway? It's not exactly like it's hard to avoid taking health damage during combat...Connor is a bit like a Terminator in his level of fighting skill vs normal people, even the regulars and "heavies".
So, to sum up...armor would make him stand out and make it hard to be a stealthy assassin and he doesn't need it because he's far more badass than everyone else walking the streets.
"They that give up essential liberty to obtain temporary safety deserve neither liberty nor safety" - Benjamin Franklin
Well if you want to argue like that, then why are there weapons beside guns (and maybe the hidden blade) at all? You could just shoot all your enemies.
What does that have to do with anything? The different weapons have different animations and add flavor to the game. The nigh unnoticeable difference in the armor rating and weapon rating doesn't do anything except for tell you "Oh hey you has 1 extra point of defense, bro."