Mechanically, there's no reason not to allow sleeping in armor, and forcing rules on it has only lead to justified paranoia (which is worse than unjustified paranoia) in my players, since I'm obviously trying to catch them with a penalty. Often, issues with 'sleeping in armor' stems from the issue of excessive resting, so look to make sure you're not allowing long rests more than once a day, and providing more frequent/smaller encounters between short rests that make them feel OK to push forward. Let the dungeoneers dungeon their dungeon. Swimming in armor is handled in the rules, so I'll skip that discussion.
That said, there isn't a mechanical penalty. I didn't say there couldn't be a roleplaying penalty.
If you want players to take off their armor willingly, there needs to be a benefit tied to doing so, and the GM needs to adjust as well. Cities are a good place to do this, not dungeons. Fights in a city should almost never be to the death, and NPC's can be unnerved about heavily armed, armored, and gorestained murder-hobos roaming around like there's always a fight about to break out. Have a clearly bothered NPC explain that "Maybe you shouldn't dress like you're ready to kill everyone you meet", and the party should happily start to trade in for some more subtle or appropriate options when they're not in a dungeon up to their eyeballs in tesla-enhanced ghouls. Make them play the 'fashion game' when dealing with civilized society, and things should liven up a bit.
City adventures can readily hinge on subtlety, investigations, and opportunity. It shouldn't be too difficult to create an opportunity where the party can enter an area unarmored, but undetected, or they can go back for their gear and lose the element of surprise entirely. If they go for the stealth route, avoid harshly penalizing stealth failures. Traditionally, every GM knows the cleric or fighter is going to find a way to knock over a hanging chandelier and wake the dead in a half-mile radius when it comes to stealth, but it's also in the GM's power to play down those guaranteed failures into opportunities for the party to single out obstacles one at a time.
Getting players to take off their armor requires them to trust their GM, insofar that it doesn't just turn into a cheap gimmick to attack them when they try to rest. If you incorporate it as part of the adventure and tune it appropriately, there's a lot of fun to be had for everyone, with or without +3 plate.