Modern landfill techniques are actually quite scientific and regulated. It's not as bad as the far left portrays. We do need to encourage more reusable things though. Plastic and aluminum can be almost 100% recycled. Plastic is much much lower. It will take more than one solution to fix the problem. I think composting is a pipe dream though unless someone figures out how to quickly do it on a very large scale. It's fine for home gardeners but the rest of us simply aren't going to do it.
Composting is only a pipe-dream for plastic because so few councils have a plastics composting process in place. No one was ever expected to compost PLA at home, and it's definitely just a feel-good exercise right now. Most PLA cups end up in landfill because they can't go to the normal recylcing plants.