Running through it in my head, the largest hurdle seems to be the pinching motion required to scrape off a blade or tines. I can imagine someone being able to support a utensil from underneath, move it slowly in the right direction, but not able to apply enough pressure to clean it. It might also be harder to keep hold of a wet utensil in water, or it might be impossible to bend over to fill and unload a dishwasher.

Of course, it could be as simple as just saying that you have to feed yourself, but you don't have to do the dishes. Someone might be able to do 10 things a day, but not 20.