Upon reflection, the most ridiculous push and start episode that I ever got involved with happened at Shannon one evening.
I was parked alongside a Channel Express Electra who called for "Push and Start". The only snag was that he had neither a tug or a towbar. Why?
Because the only available tug and towbar was already connected to my aircraft and the chap on the headset told me that they were going to push me back and then go back for the Electra!
At Shannon the tower can't see that part of the airfield so my request to "Push and Start" was refused because the Electra had already been cleared.
The next few minutes were like a sketch from Monty Python.
Eventually common sense prevailed but the point surely is "How on earth can you call for push and start when you have nether a tug or a towbar"?