Coppers do warn against answering the door holding a weapon. Not that it might offend them, but they might be knocking on doors to warn you about something in the area. They do say it is OK to have a gun within reach of the door. Like maybe near where you would retreat if confronted by a criminal on your threshold.
So, you open door, creep shows you his gun, you retreat and grab yours. Either slowly so they can rethink their plan or just fire away.
Yes. Everyone should be capable of being armed at a moment's notice.
Have kids? It is your responsibility to teach them how to be safe. It is not an accident if they go to play with one of your guns and someone gets hurt -- you dropped the ball.