If we are basing solely on the premise on whether or not we should keep the durability system as a consequence or punishment for bashing doors and chest open then I don't believe we need it.
Currently many people will avoid this by either using worse weapons, magic, or save scumming and most implementations will have people taking the chest to a remote location out of sight and just going full hadoken on it.
So what can we do to make opening doors and chest in unconventional ways(ie without a key or lock pick) more interesting and less time consuming?
First lets figure out the states in which a door and chest can function as:
1)Most doors and chests will be found in a locked state. It's function is to keep unwanted or perhaps a better way to phrase it would be an unworthy person to open it unless a condition is met.
2)The second state is opened. This is the desired state and after the initial state change it loses almost all value.
So I believe to reduce time on dealing with a chest or door, there should only be two states it exist and that is open or locked and that trying to spend years breaking a chest or door to be an unnecessary state. With that in mind lets figure out on how to make it more interesting.
In opening a door or chest we go through a process of elimination on how we should open it. First we would try to just open it with the assumption it might be open. Second we would look for a key. Third we would try to lockpick it. Fourth we would look for some weak point that we could pry open. Fifth we would try to break the the lock. Finally we would go barbaric and either try to bash the chest open or blow it open with magic.
To make door opening and chest opening interesting I suggest we have multiple different answers:
1) If you are a warrior you would need a certain amount of strength and a proper weapon to break open a chest or door.
2)If you are a rogue or archer you would try to spot a weak or vulnerable point in a chest or door and try to pry it open with some finesse.
3) If you are a mage you could have several different ways to open a chest or door. A user of pyrokinetic could force open a door as long as they had the right amount of skill and know the right spell but would burn all contents in a chest. A user of hydro spells could freeze the lock on a chest or door and have a companion break the lock. An aerothurge would require immense investment into that stat to break open a chest or door. A geomancer could easily throw a boulder through a door, and use poison to corrode a lock on a chest and the list goes on.
So with this solution we will prevent the need to save scum or move chest around to break them open, save time from smacking or burning chest and doors, and make it more interesting to play/build around with a simple check.