Man, that was one long, weird, post.
On a schedule based on average traffic, the cartridge is replaced on a schedule, which can be months apart. Someone puts on a glove or not, removes the cartridge and pops the new one in, just like they do with the ammonia cakes and the cigarette screen
Every night the janitor sprays it as you are supposed to and wipes the porcelain just like he did the old urinal and the toilets.
The toilets, lavatory sinks and the ladies room all supply plenty of water for the sewer line.
You were describing nothing and trying to make it sound like something huge.
Not everybody has a janitor on a nightly basis. Many clean on a weekly basis.