Another thing to consider, and one reason I'd be unlikely to shoot through my door, is that you do not know who is on the other side, where exactly, and why.
While rare, police have been known to execute no-knock raids on the wrong address. They tend to do these in the wee hours of the morning and start by bashing in your doors. If you fire on them they are going to kill you. It's a tragedy for your family but they will walk away from it.