The last couple of towns I've lived in didn't have municipal trash pickup or mandatory anything - you can pay a private hauler, or take your bins over to the transfer station yourself. I make the transfer station run on Saturday mornings. There's a separate recycling building (the former town was sort-your-own, where I live now is single-stream) from the trash building and both towns elected to create these structures because the recycling was a way to recoup money rather than dumping in landfills. The sort-your-own facility actually posted the $-per-pound of each type of material and urged us to drink beer from cans rather than bottles because the town got more money for metal than glass.
It stretches credulity to think that some company is paying the town for its recyclable material only to turn around and dump it in landfills. I don't doubt that there are many places where, the way the system is structured, the kind of scam @two fingers described is happening. And clearly there's the issue of matching the material with manufacturers who can use it, which will never be exact (and I understand is particularly difficult right now). But maybe the better way to think of it, in the big picture, is as an efficiency problem - what percentage of material we try to recycle actually gets recycled, and then what can we do to improve those percentages? It will probably never be 100%.
I also agree with the issue that you can't put all the onus on the retail customer, you have to have more responsible behavior on the production side, especially as regards packaging. It really struck me when I bought a volleyball net last summer; it came in a box with the components all wrapped in plastic and padded with styrofoam. If I had a choice, I wouldn't ever touch styrofoam, and I certainly wouldn't go to a store and say, "I need to buy me some styrofoam today." The stuff is noxious. But I literally have no idea where I would buy a volleyball net that WASN'T packed in styrofoam, and even if there were more than one option of net in the store, there's no way I would have known that THIS model was packed in styrofoam but THAT one was packed in, say, something biodegradable. I'm not allowed to make a free choice as a consumer because I don't have the options and I don't have the information I would need, if I wanted to make a styrofoam-free purchase.