I’ve worked in hotels my whole life and yes I was trained in housekeeping. For checkouts anything opened is tossed. That is anything that is the hotels. Housekeepers should put all opened shampoos that aren’t in the hotel into a lost and found bin.
If the room is a stayover they hotel has guidlines on when to replace them. The upper scale ones will replace them everyday regardless. Some wait till the soap is 2/3 used. Etc.
BTW you can always tell how honest the housekeepers are by the quality of stuff they turn in. When I first started out in 1982 we got great stuff turned into the lost and found. I got a London Fog trench coat, a bike, a couple of Brooks Brother’s coats. It was cool.