Interesting question. Believe me I'm no military expert but the strategic value of motorized infantry is two fold:
(1) Speed. As you mentioned before, this is probably the greatest advantage.
(2) Towing capacity. Obviously trucks, motorbikes and the like optimized for military usage have a much greater towing capacity. They are able to deploy heavier equipment, weapons or provisions into the field allowing infantry to spend more man hours on the ground. Otherwise foot soldiers would rely primarily on...well foot. Marches. Some trucks may have pintle mounted weapons like light machine guns or grenade launchers.
The problem is that many motorized trucks that are not cavalry (i.e. tanks, APCs, IFVs) are not armored enough to provide a real tactical advantage in terms of infantry engagements. But the greatest power lies in rapidly deploying forces to areas of need allowing quicker and more precise responses to enemy advances. In other words speed and carrying power are probably the biggest advantages.
Take a look at these:
German Armored Recon. Vehicles
Soviet armored car