Does a frame/wheel lock that can be locked without the key being inserted exist? And if so, how secure is the lock itself (I heard that this style of locks that can be locked without the key inside are more susceptible to picking than normal style locks)?
These locks are variously named ring locks, cafe locks, O locks and defenders.
Update: There is another style of lock that is similar to the one picture above, but it has a straight locking bar instead of curved one. This type can be locked without the key inside, but it's not as easy to close and open due to the bar not being curved.