As is so easy to do in this situation I think the conversation is blurring the lines between checks and checklist. What I was trying to say is, in my company all after start checks and the checklist bar two items (flight controls, ground clearance) are completed while waiting for the engineer to disconnect. This means that at no time during the taxi are you conducting checks, just a three item before takeoff checklist. I think this is an improvement on the old way we did things which included a flight control check during taxi.
The concern people are expressing about delays while you sit there blocking the taxi way while you do checks is not necessary. I don't see that it causes any tangible delay at all having done it both ways.