They already do this. Some news organization did an expose on it. They went through a building that was simply corridors full of one-room offices, a company nameplate on the door, and no one ever went in or out.
And there were lots of those buildings too - all one-room offices all dark because no one was there. But the office was there to show presence. It was really quite a depressing scene - all around the courthouse are dozens of office buildings which are fully occupied, but whose population was zero as there was no one actually in there.
You sorta wonder why they bother running air conditioning or lights.