If John Harrison were well acted as John Harrison then the audiences would likely go along with it.I think that would have been a huge minority. There were TONS of trekkies that were pissed Khan was in this movie.... and the new movie goers who didn't know who Khan was were "who the hell is Khan?" when Cumby made the big reveal.
"Real Spock?"and Spock yelling Khan... eesh. ...then Incredi-Spock going all Marvel at the end to catch Khan. Real Spock would have used his brain. Totally out of character.

This Spock endured the destruction of his entire planet, then looses a commanding officer (Pike) and then looses a developing friendship (Kirk). The specter of death hovers around this Spock and you expect him to behave logically?
Talk about straining suspension of disbelief.
I agree. That's why I think Khan was not really needed. I'm willing to go along with it, but I personally love Marcus as the villain, as an admiral who feels that Starfleet is outmatched and needs an edge. Khan's inclusion was not really as important but I can work within the film with it. I just think, as you noted, the reboot would have benefited from not referring to Khan, and that Trek itself needs to move away from TWOK's shadow.I think the point of a reboot was to be able to not be constrained by, even overly influenced by, the previous stories rather than getting to be very influenced by them, redoing them, that a reboot allowed you to go in a whole lot of new directions.