Lots of people take food back to their room at Poly and all CLs. There aren't really disposable dishes at Poly, except to-go coffee and drink cups. They used to have small paper plates and bowls for the kiddos, but I don't think I've seen those much anymore.
As others have posted, many people will just leave plates in the hall, which personally bugs me but to each their own. Disney doesn't have staff roaming the halls to pick this kind of stuff up, so sometimes you'll see dirty dishes out for an extended period of time, in my experience.
We try not to bring too many dishes back to begin with, but when we do we leave them in the room in the coffee maker area, Mousekeeping takes care of them. Sometimes we'll take them back to the lounge, Poly has a small "dish return tray" usually out by the door.
The below is a somewhat common sight in the Hawaii halls (note, this was NOT my room!). The evening app "small plate" style definitely adds to the plate count these days.
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