If you read it again, even the presorted gets sorted one more time.
It is only presorted by route/delivery driver. The driver actually sorts it again.
That is correct. All of the bulk rate stuff is delivered in bundles that have to be broken down and added to the presort at the delivering post office. So while the regular mail is presorted by delivery, the contractor in the rural areas will probably still recase it to add the bulk mailings and then put it back into the trays.
None of the vehicles have the space to do that going down the road without slowing the route delivery and ... pissing people off who expect their mail to be delivered at a certain time.