Try to take apart a box where you have half-empty yoghurt cups and newspapers.

And now imagine having them separately.

Separation by the consumer is far easier, because they can make sure in the paper container is purely paper, and it can just be dissolved, cleaned, and recast into paper. And in the plastic container is just plastic, metal and organic stuff, so you can clean it with water, and are left with plastic and metal, and can separate magnetically.