It isn't necessarily the worry about breaking the latch, as it is now the inability to prevent entry without it. We have a teenage daughter, who like most teenagers, is slow to get up in the morning. If she comes with us, hubby and I would often be up and dressed, then head to food court to grab breakfast while she got ready. We would have the DND sign on door, but she would not throw latch since she might be in shower when we returned. She's of sufficient age to be left alone in a hotel room while we go to the lobby area for food, but still a minor and still taught to not open doors for strangers (actual instructions are to ignore and pretend you aren't home, so they won't know she's home alone).
Now, if we were to return with her, we would end up skipping breakfast and waiting in the room for her then heading straight to a park. I do not feel comfortable leaving her in a room alone when housekeeping or security could knock and enter the unlatched door. If she were to respond to a knock, which goes against the normal ignore policy, who knows who it really is out there that she might be talking to. Seriously, some people have thought the policy was because of trafficking and have posted links about child predators so why SHOULDN'T I be concerned with her talking or opening a door to a stranger at the hotel? If she were to latch it, that means we could end up waiting outside the room for her to get out of shower. And there is no guaranty that a latched door would stop a CM. While I haven't seen reports of it, if they won't use their latch-opener when no one responds and the door is latched, then why bother opening it to begin with?
So as I said, with those being the two scenarios of stayng onsite that include breakfast, we'd just skip it rather than leave our teenager in the room. Staying offsite next trip makes everyone feel safer, which is a sad statement to make.
