if rolling friction simply rolls over the irregularities, what about the irregularities on the wheel, don't they get stuck with the ones on the surface?
When a body rolls on a level track,the contact area is very small,so pressure exerted is very large.This causes a depression in the surface below and a mount in front. In turn the surface of a rolling body in contact gets slightly compressed. A rolling wheel constantly pulls out the depression and goes uphill on the mount ,simultaneously detaches itself from the road.but this process is so fast that there is no effect of irregularities.If tyre of wheel is properly inflated,it gets compressed by the road to much smaller extent.Due to reduced rolling friction tyre of wheel move easily.