Yes, it makes sense to wash your hands before you eat. But since when is it the governments job to mandate it???
If you want to take advantage of government programs and facilities like public schools, you have to follow certain rules. Many of those mandate certain actions to increase safety or public health -- vaccinations in schools, seatbelts on public roads, etc. An increased emphasis on cleanliness -- and perhaps some hand sanitizer dispensers in the lunch lines -- might serve as an inexpensive prophylactic for all those school germs.
For the same reason that we mandate things like immunizations. People who don't wash their hands are carriers for diseases that can infect the rest of society.