Only one housekeeper cleans an entire floor?

One housekeeper per station will clean a floor. For example, six floors of hotel rooms, one housekeeping station per floor. If you build a service elevator connecting all six floors, six housekeepers will clean each floor, they just originated from different stations.

My experience has been that 2-3 stations are good enough for 6 floors. It sounds like your hotel may be wider, so you may need more.
I believe you need service elevators, stairs will not work. They're not dragging those carts up and down stairs.

If you don't have six floors of hotels, then you can watch the housekeepers sit in their stations and not do anything. Lazy.

I know this post is super old, but I always read house keepers will not use stairs in this game. They will actually use up to three sets of regular stairs to reach a floor!

This means you could have one cleaning station for three floors of hotel rooms. Whether or not all the rooms will get cleaned is dependant on how many rooms per floor; each house keeper will clean up to 19 rooms and only one house keeper from the station will be assigned per floor.

It seems to be pointless to use stairs for housekeeping, you're gonna end up needing that service elevator.