"wide open" does leave some interpretation. Some closers don't close hard enough to latch the door. There are arm closers and there are spring loaded hinges, either can be disabled so the door does not close on its own. Sometimes housekeeping uses the flip lock to keep the door from latching.
Once the door is closed and locked I am sure occupants and goods are secure. But if you need to leave the property, you are at the mercy others know to close the door behind them. If that is beyond the ability of property staff a new property is in order.
I you find your door is open when you arrive and no one is visible, DO NOT ENTER! If you don't recognize the person in your room DO NOT ENTER! Go to the nearest house phone and call for security to check things out. Even it it's someone that is working on the room, don't risk confronting the person, keep moving and stay away until resolved.