The Maya were a class society. The nobles and the priests were the highest class.
Each city had a palace that housed the city ruler. The rulers lesser relatives had homes of their own, or lived in the palace. The palace was built around an open area. That gave the nobles a place to get our side that was private. In their own garden, they did not have a servant who held a cloth in front of their face, as they did when they went out in public.
Each city had a temple. The temple was a place of worship and a home for the city's priests. The temples also had a central courtyard, where the priests could find some privacy. Pyramids were tombs. Temples were homes.