I think to make the "bigger tire is faster" theory a reality, requires a more powerfull controller in many configurations. Lets say your cart with an upgraded 500 amp controller will do 25 mph with 18" tires. That controller can still move that cart faster with a better gear ratio (or larger tires). So, if you now replace those tires with 23" ones, you will see the speed increase to say 30 mph +/-
That stock 250 amp controller, just can't get those bigger tires moving much faster than the 18" tires.