So you want everybody to have protection, yet not good protection?
The matter of fact is that lockpicks render locks useless.
By making them unpickable when you're offline you're only causing more thefts happen when both parties are offline - causing more outright conflict.
Also, giving a 20 minute period after you leave to have the locks pickable is pointless - people won't want to log off because then everybody would race to their house and steal from them (which is exactly what would happen).