So the sticking points are non-drivers, HCTs, and a general increase in "stuff" you have to delivery if it previously didn't go out.
Even for a van share...not going out everyday means more letters in each bag (bundles of mail). More letters means more weight and more steps equals more fatigue and more time doing each loop. More letters also means less room in the pouch for packets. If you start kicking out packets to be able to fit the letters in you'll have to run round after the loop with packets using the van which adds more time per loop. More little packet piled up in the van means more chance of missing something that's disappeared in the van and having to double back to the previous loop to delivery what was missed (well, at least the tracked ones!) - which means more time.
Even if you redesigned the loops so the walker's loops are longer to handle the mail side but gave them a LWT and the driver does more packets you probably will not speed anything up. The walker will have more fatigue with more steps; and the driver will be worn down getting in and out of the van (if you have never tried getting in and out, and in and out, over and over, it is very wearing) and obviously packets takes a lot longer per drop as you're knocking on doors waiting for an answer and writing cards out so the time increases.
Overall the day is a lot longer and you're more worn down. If the heavy day is followed with a light day maybe it's slightly more doable but, it may not work for everyone or office.