I see two big things that others have touched on. One, you wll not believe how much of a difference a real road bike makes in your speed once you have a chance to try one, and the average speeds you're seeing are almost definitely on road bikes.

I'd say it's less the bike and more the tires. My "city bike" is a rigid mountain bike from the '90s (edit: which is also extra-heavy because of basket/rack/panniers/fenders), but because I put smooth-ish (but still wide) tires on it, I cruise at maybe 15-20 mph on flat ground. Sure, the handlebars/riding position and (in OP's case) power losses from the front suspension make some difference, but not nearly as much as the tires until you get going really fast.