The certain item used to open these are difficult to find. Sometimes, if you're a rogue, you'll find doors by mistake while testing locks and the thing will be destroyed. I suggest that instead of immediately using and thus destroying these things, it opens a conversation giving you the option whether or not you wish to use this thing to open the door.
This would also keep you from wasting these things by trying to pick the lock on the inner doors.
You can also drop the item from your inventory before attempting the lock.
I don't have the time to do every lock I encounter that way...
Not going to happen, I'm afraid. There aren't very many of this kind of door, just learn where they are! :)