If that illegal behavior does not seem to be likely to harm either the room or other guests, I feel like the people who are saying that not only "the correct thing" for a hotel to do here but "what I expect most hotels to actually do in this situation" is to, if they do anything, at most alert local law enforcement and cooperate with them if there is an issue, not decide to send hotel employees to go run an internal investigation to verify the activity even is illegal in the first place, after which point I guess the idea is you want to send the bell hop and the concierge and the night security officer to go evict them from the hotel?... This just isn't how anything is done and is asking the wrong things of the wrong people leading to situations that are super dangerous for everyone involved.
Meanwhile, it isn't even "in the public's best interest" for the hotel to act as law enforcement as the most they can do is evict the person from their one hotel, not actually stop them from doing whatever "illegal behavior" is taking place. (At this point, apologists for monopolies probably start arguing that this is why we are all better off if everyone is forced to use one or two providers, so that everyone can be forced to fall in line with whatever the new corporate vigilante justice rules are... sigh.) Law enforcement is empowered, trained, and equipped to actually do something, not the hotel staff.