Buy or make better quality bags.
I don't expect most people to be able to manage what I did in making my bags out of industrial scrap from the parachute plant I worked in, but its not beyond the moderately-competent home sewer with home equipment to make bags by recycling the good parts of old jeans or buying cotton canvas. Bags can also be knitted, crocheted, knotted via macrame, or even made from duct tape (available in colors and patterns specifically for crafting (but probably not washable)).
You could even use old pillowcases.
I don't use them on principle, I use them because I shop at discount stores that don't offer bags at all. Its not nearly as big a deal as people make it out to be.