cb9002 Two main reasons: Firstly, if you start an engine at the terminal, you would have to prevent movement of people and vehicles in a wide area in front of the machine. For many places this would bring the whole pier to a halt - as the vehicles are running up and down in front of, and under, the pier to service everyone.
Secondly, the risk of the engine sucking up waste/trash material lying on the ground would be very high. There would be plastic and cardboard and other stuff lying around near the terminal and that can kill an engine fast. Which is why the a/c was backed off the stand to start an engine and attempt to cool the a/c. As has been stated by Ignition Override, the chance of a single engine being able to do that with an overheated airframe are low.