In many cultures, people below a certain social class aren't allowed to wear metal armors or wield certain weapons period. Even in a place where you might legally be allowed to do so, if you are a lowborn character walking around in full plate that raises a whole mess of questions that the NPCs of the setting will be very curious about. It would not be at all uncommon for NPCs to be incredibly suspicious of the character. Where did your character get this? Did he steal it? Murder for it? Gods forbid, he looted it from a battlefield. Filthy grave robber, that. Carrion bird. Worse, why are you wearing it? What good, civilized person is walking around in plate armor? I bet he's up to trouble. Why would you be walking around in armor if you weren't intending to get in a fight? Someone should alert the guards. Probably some kind of brigand.
And of course, that's just begging for the local guards to harass you constantly, because you look sketchy as hell. The Nobility will probably also be upset at you, because here's this common filth dressing themselves up like a noble. They dare presume to appear above their station? Someone ought to teach them a lesson.
Imagine you find out see someone at the mall in full tactical gear with an AK47 held low and ready -- you're going to immediately assume something is up. Imagine that you find out your neighbor has a full assault kit and explosives in their basement. You're naturally going to question if they are up to something.
If the GM finds that their players are building murder hobos, then the GM should feel very free to let the society of the game react accordingly. All of this is, of course, not even touching the fact that plate is not only ridiculously expensive, but also costly to maintain, difficult to get on, etc etc. It's actually a spectacularly poor choice for anything other than battlefield combat in which one knows when and where they will be going to the battle.