I used to reuse the plastic shopping bags as trash liners for small cans around the house. Since they have been banned I have actually had to start buying bags for home.
I do hunt out extremely cheap thin bags that probably use less plastic per bag than the grocery store ones as they don't need to be as durable for most of the cans. But I also use heavy real garbage bags for the kitchen trash whereas before I'd use a grocery bag and empty it more often. So I can't really tell if I'm using more total plastic or not.
They were recently saying that they've started to see more and more of the other residents using the much thicker bags now sold at checkouts for bundling their garbage, rather than the thinner plastic bags they used to use instead.
We split our garbage into compost, recycling, paper, glass, and others.
Compost goes to a compost facility that generates methane from it and then sells the excess as fertilizer. Plastics get recycled. Reusable glass bottles get cleaned and reused, other molten down and reused. Other gets burned, filtered, and generates electricity.
When they raise it and turn it upside down to empty it, the wind can easily cause any loose and light stuff to blow around and not end up in the truck.
One bin probably is a small thing, but I can definitely imagine if the entire block were doing it it would start to accumulate fairly quickly.