I'd love to hear the logic, too. The only thing I have heard is safety -- that there are vehicles on the road and maybe snow plows, not looking for traffic/bikes. A pedestrian is only marginally safer, so you are right, it makes no sense.
It sounds to me like we (worst case scenario) could also just leave the bikes packed and continue on hiking on the road for 9+ miles to the National Park gate and then take the road from there to Jacob Lake? Is that how all the hikers and skiers get in to the North rim?