Hey, I've got a solution to this.
Hang up a sign in the kitchen with big letters spelling out all the steps involved in washing dishes. Tell him he's not a toddler, and he needs to learn how to do this. There's no better time than now.
He really DOES need to learn. What will he do if/when you're in the hospital? When you're off on a trip for work? When/if you have a broken leg & your doc says lay off of it for six weeks? There can be all sorts of reasons why you can't be there to take care of him 100% of the time.
You're just teaching him the "life skills" he should have learned in the home he grew up in.