What could be more interesting in technological terms would be large, well-balanced long-range wheelbarrows. They could replace mules on roads and can move at the speed of infantry.
Actually, I don't even think the wheels are, just the tires, and the axle. As for the drivetrain, well, you could at least make a penny-farthing-type design, with the pedals directly attached to the front axle.
As carlton_bach observed taking your kit with you is more useful than doubling your speed, which is all you would manage with any form of bicycle. When I was a lad we took all of our kit for a camp on the boy-powered trek-cart. We went for miles and not just on roads, farm tracks and across fields as well.