Their crew numbers aren't actually that high, though, for warships. About the same or a little lower than Honorverse ships. Now certain PF makers ideas about what it is crew are used for is a different issue. You only have crew numbers that high if redundancy is a primary concern. Redundancy is not a concern for cleaning, so the crew numbers are either wrong or they are doing more than cleaning.
5000 people on a battleship suggests that needing to have 5 people who know how to fix a single part on the number 4 laser when it breaks is a rather high priority, just in case four of them already are dead. You need people rather than programs to do that sort of job because they have to think on their feet. Automation and drones cut down on the number of people you need, but you still need a lot of brains. I think the rogue drones are the only EVE examples of that level of automation.