Bashing the alchimist chest with bare hands takes time and will attract monster so that's good.
However I do much more damage with hands (up to 10) than with the Iron dagger that never goes over 3 or 4. And it is fair to lose 1 HP each time you smash something

There should be a mode when you do not really bash the barrel but rather try to open the top so it should not need to put it to 0% condition. You should still have chance to break your tool. I had no option to try with axe or such like so I do not know if it works better.
However contrary to another post I could not do any damage at all on the reinforced door upstairs in the inn probably because I am not strong enough so for me that part of the process is just fine.
Maybe some others comments on that topic ?