Bob, if I never primed prior, my generator would require excessive cranking to start. So I don't know what more to say.
There is no hard fast rule for everyone because Onans seem to behave differently from one unit to another. I suppose it comes down to finding what works best for your PC.
Ron, I think you are right in that each generator may behave differently. My 2010 Onan was difficult to start after priming and after I read the manual regarding priming and starting (see below) I no longer prime and it now starts perfectly. I was told to prime before starting and that is why I was doing it, but now I don't. If someone is not satisfied with the way their Onan starts they might try it without priming if their manual reads as mine does.
PRIMING THE FUEL SYSTEM
If the genset ran out of fuel (gasoline models only)
prime the fuel system by holding the control switch
at STOP/PRIME for 30 seconds. (The status indica-
tor light will stay on while the pump is on.)
STARTING THE GENSET
Start the genset from the genset control panel or re-
mote control panel inside the vehicle (Page 1-4).
1. Push and hold the switch at START until the
genset starts. The status indicator light on the
switch flashes while cranking. It will stay on
continuously when the genset is running.