Then why do I have to add all those "No unauthorised access permitted" warnings on routers? They are password protected.
But to get to your example, it is a faulty analogy because the charge would not be burglary. Burglary only occurs if a theft takes place. An unauthorised entry charge would be "trespassing". If the lock is broken on entry or damage occurs, then it is vandalism or criminal damage.
HOWEVER. The reason for the router warning is that unless you explicitly say unauthorised access is prohibited, then it isn't even trespassing.
To use your analogy. It could be argued that if you leave your door open it is an invitation for others to enter. If an open door requires no active measures to gain entry (a handle being manipulated or door pushed aside) and there are no signs saying that access is forbidden, therefore permission is implied. Not to steal or vandalise, but just to enter. If you find that person standing in your living room and that person is then challenged and asked to leave, but do not do so, that is trespassing. If you don't ask them to leave, it isn't (hence warning on routers above).