Stop asking awkward questions....
You have a good point but this one probably comes down to economics: if we stayed put on the gate after the doors were closed so that Cabin briefs and checks could be done prior to taxi then it would slow down the whole departure "process". Not only would it delay the flight going out it would possibly deny the use of the gate to inbound aircraft.
Having said that it a good idea for the crew to spend as little time walking around as possible and behoves us at the front to keep the taxiing as gentle as possible.