Illnesses? Yes - besides diaper rash, he and the family are at high risk of E. coli infection and other diseases caused by bacteria in feces. There is a ton of stuff out now about simple but thorough hand washing and not using antibacterial products because of the Ebola hysteria, flu season, even kids with severe allergies due to cross contamination. Soap and lather for 30 full seconds, then a rinse, will take care of it. But he's got to have the importance of this impressed upon him.
You can wait for peer pressure but that may take a while and it sort of invites bullying. I'd do some of the things listed below. A hygiene book that deals with puberty and body changes. That will cover all forms of body odor and encourage showering and thinking about armpits. If he doesn't want to read the book, I'd assign a book report. Really. He'll have time for that when you take away TV, computer and after school activities.
It's "too much work" may be his excuse - perhaps he's really scared of the germs involved in wiping? I'd teach him about hand washing, remind him that parents all over the world change poopy diapers, and assign him a 3-wipe limit (wipe, fold, wipe, drop in toilet). You can buy disposable gloves if he won't put them in the toilet. If you don't want any wipes at all in the toilet at all, you can put a supply of plastic bags in the bathroom. You don't want to make him obsess about bowel movements so much that he holds in his poop, but you DO want it to be more work to do it his way than your way.
The next thing you do is put him in charge of all his laundry, including stain pre-treatment of all underwear. He's not too young. My son was doing laundry at 15 just because he was in sports and I wanted him prepared before he went to college. Get him his own hamper so his stuff doesn't contaminate everyone else's laundry, or have him run off his own stuff along with other people's stuff so he has a full, energy-efficient load of wash. He can dry, fold and put away. That ought to make him aware of how much time laundry takes (ideally appreciating the adults' efforts in his home) and also make wiping seem like a small investment in time.
You can either stay in the bathroom with him, have his father do that, or have him meet with the pediatrician or nurse to refine his technique. He can talk to the health director or coach at school. Ask him which he prefers.
But unless you think there is a real phobia attached here (requiring a therapist), vs. laziness, I'd start taking away far more privileges. If it were me, everything else would stop until this was dealt with once and for all.
