I agree with those that say the cost of bashing open a chest outta be a potential for broken items. Also the "broken items" should be shown to indicate that you are missing out by bashing down chests.
The cost bashing in a door needs to be handled exclusively, with reactivity mechanics. Bashing/burning down a door is louder and takes more time than a lock pick, there should be a significantly greater chance of being caught while doing so. I think in the ideal case, every time a door is hit there is a chance that near by NPCs will notice. If they are on the same side of the door as you and they notice, they would recognize what you are trying and sound the alarm etc. If they are on the other side of the door, it is a bit more tricky but I think at the very least if you bash the door all the way down, and during that period somebody noticed you bashing/burning, the alarm would sound. The chance of being noticed could be based on distance from the bashing, and Wits of the characters. There would have to be very clear feedback about when you are "noticed"
As a note, I also like the idea of weapons only being damaged for the duration of combat, so that there is an opportunity for gear destructive skills, weapons, strategies. For example an enemy could have some powerful sword, I have high Loremaster/Wits so I'd know what the effect the sword is having on his overall abilities so I target the sword directly. The biggest challenge with this addition in my view would be the UI complexity for handling all the different gear durabilities.