My father in law says the same thing.
I have a couple of self propelled mowers and a couple of push ones. My 3-speed Lawn Boy in 3rd gear will pull me around the yard-I get winded trying to keep up with it(the single speed of the same generation I've been known to crank up the governor partially to get ground speed a little higher). I THINK that commercial Toros still use a similar 3 speed-it may be the same one for all I know-but that's probably more than your friend wants to spend.
I've used Toro Personal Pace mowers and I've used Hondas with the thumb twiddle. I'm not a huge fan of the latter, but both can move at a pretty good clip if you wind them out.
Aside from that, there's nothing that says you have to use the self propel drive.