My bathrooms in Australia have central drains but painted ceiling, cabinetry that isn't entirely waterproofed, etc. I wonder if you could automate the cleaning and drying (blasting hot air) like some new public toilets or a dishwasher. Put away towels and trinkets, walk out, close the door and press a button.
Hell, even just self-cleaning toilets and basins would be a start.
My wife's family, in Iran, has a drain in the middle of the floor for this reason. She think it's very strange that this isn't common here in the US.