The eggs are deposited only UNDER the skin. The scabies don't lay eggs anywhere else. You are correct, they will die within a week without their blood meal.
In fact, when I was infected, I used this principal for all of my clothing. I wore shirts that were from the bottom of the pile & clothing that had hung on hangers for more than 1 week, to be certain the scabies, if any, were dead.
You are also correct, they do not live in carpets or around the house, so it is a waste of time & money to put DE everywhere. However they may be located where you normally sit and work, so that DE in these areas will help.