The stores in CA where plastic bags were banned now have insanely THICKER plastic bags they charge you some small amount for, and they claim are reusable.

They are really thick, almost as nice as hardware store bags, but they all get thrown away.

They should have require a standardized bag/crate with deposit that you would use instead, make it durable enough and people would bring it back or just throw it on the sidewalk and enterprising youths could collect them for the deposit.