Somehow I don’t think cloth/canvas is going to be any better to clean than slick plastic. Actually, no, it’s worse. Just that if you have cloth it is “biodegradable” whereas plastic is not.
I have cloth bags labeled for Save Mart and WinCo Foods. Have no problem keeping them clean—I just wash them in a sink with warm, soapy water and then air dry them.
Cloth bags can be tossed into the washer with soap and bleach. Why is that not better than plastic?