There are rules for this!

In the 5e players handbook, under chapter five, there is a subheading called lifestyle expenses. This details some possibilities on how people should expect to live depending on how much they pay and provides some good tips for doing so. For instance, perhaps the town mayor had an important mission to undertake, but when these "heroes" living in the street, with rumors being spread about them, in full armor, show up, he may refuse out of distrust. 

Also, sleeping in armor is incredibly uncomfortable. Even leather is hard and rigid in armor, and if they try to sleep in it they could suffer from exhaustion because of no good sleep, and if they take it off, they could wake up with it all missing next morning! Think about what would happen today if a bunch of people just showed up in a suburb and started living on the street. Real consequences are almost always fair and immersive, except in extreme cases