It's the propped doors that are a noteworthy security concern for me, not the honesty of the housekeeping staff. So many times you can go down the hall of a hotel, the door is fully open for ease in cleaning, someone's stuff is visible all over the place, but the housekeeper is not within sight for whatever reason.

And I'm in the camp that says that you can reduce petty crime by 80-90% by simply making it slightly harder for any potential criminals who know that if it takes more than a few seconds, it's not worth it. So anything of significant either gets buried in a closed suitcase or put into the safe when I'm not in the room.