why not charge on the fly!
Well if that little generator can charge the car on the fly, doesn't that mean your car's engine could be just this tiny little generator? Your 13 HP generator probably can't push a car along at 70 MPH.
IMO - Plugin hybrids and range extenders sound great in theory, but it's adding a lot of complexity and stuff to maintain that can fail. One of the main reasons I bought an EV is that you don't have to worry about changing the oil, letting old gas sit in the tank, or dealing with upkeeping the emissions / fuel lines / vacuum lines and so-on. On a PE-H you just bring in all that other stuff in addition to the same worries you'd have about batteries / inverters and chargers failing. More to go wrong, more to deal with, more weight. Road trip charging is an issue to deal with, but I think range extenders, other than something you could de-couple from the car and bring as a trailer or in the trunk as an accessory for road trips aren't really ideal.
Random note about EVs: I take night classes for machining/CNC work here, and yesterday I drove to school in my EV. It was 95 degrees outside and I was tired, but wanted to take a nap before class. I parked in a garage spot out of the sun and turned on the AC. I slept for a half hour while my car stayed at 70 degrees inside and used about a dime's worth of electricity. Zero fumes, no noise, no wear and tear on engine/accessories or bearings while idling for a half hour.