Sounds like a good idea.
I've worried about little kids who ride in carts after I have used them. My daughter says someone has invented a sort of seat that mothers can put in carts, before placing their children in the carts.
Other places I've wondered about -- pharmacies, (since sick people are handling the boxes of analgesics, cold medicines, pepto-bismol etc.) and gyms (since so many people place their hands on the same handles).
Because I usually have handled many packages of beef and chicken, before picking out the ones I wanted to take home.
I can place the packages that I choose into plastic produce bags, but I don't place my hands in bags. I use my hands to push the cart and pick up other products in the store.
My 90-year old mother was the only family member to get a "stomach virus" -- the day after we went to the pharmacy section of a large chain store.
My son works as a clerk in a pharmacy, and is often the first family member to come down with the "latest" bug.
I've seen those too--here's a site:
http://www.shoppingcartcoverstore.com/
I think you can get them at places like Babie R Us as well