Hants flyer...
The engine starting is really a measure of SOPs. I've flown 737s with five Companies now and been a trainer for four of them.
Some Companies have the captain start the engines, some have the F.O. start the engines while the Captian supervises the whole push back procedure, some have the PF starting the engines, and one changed the procedure when the NG replaced the -200.
I don't really think that who starts the engines is a measure of the 'god-like figure head' in the left habd seat!!