Person from Germany here where we have 4 different bins per household - paper, recyclables (metal, plastic), compostables and dump (+ glass by color, batteries and electronics at dedicated sites). We get to a recycling rate of about 20-30% (effective at plant) with really wanting to and having it ingrained into our culture.

Recycling is hard at the best of times. Unless packaging gets much better at identifying as recyclable it will be a long road ahead (it's the small things, black plastic is hard to identify and get's burned, composite plastics are problematic, like different plastic foil over plastic canister). At least people think about it around here, but it is a very hard problem.