I agree with all of this but the one thing you didn't consider was not that hosts expect guests to behave appropriately after showing their ID, it is because if they do commit a crime, you know very well who was in your house and that person was verified by you - the most that can happen is that they presented a fake ID. This is very important for police work. That's the whole point of asking for ID's.
Someone also mentioned human trafficking. There is also the taking of minors. So it worries me that if a couple, married or not bring a minor with them, I want to know the relationship and the name of the minor too. It could well be that the adults are the minor's aunt and cousin. But we all need to keep our eyes open for criminal activity that happens right under the noses of many hotel and motel rooms. Well hosts are not hotels and motels, we want assurance that the minors who may be brought along with a couple are truly the legal charges of the adults. If the minor isn't related and is just gifted a free trip, then we could at least have a name.
There is too much crime, we don't need to want to facilitate criminals if any of our guests just so happens to be one. It can happen to anyone. So this is so much less about property damage than it is about personal safety of the host and any minors who are tagging along with adults.