FJJP. I've done it. But it was an operational neccesity, and I didn't waltz up to the engine like your liney
In this case one of the breech caps was u/s, the little electrical contact tang had broken off. So the only way to get the stbd engine started was to swap caps with the port engine up & running. Maybe the difference is that I told the pilot I was happy to do it, was he happy? He was. (it was away from main base)