Japan, or certain cities in Japan, have pretty complex recycling rules, at least relative to California.
You're required to separate glass, PET plastic, other plastic, aluminium, clean paper (books, magazines, newspaper), burnables (food, soiled paper), unburnables, and then also large items and electronics require extra fee and an appointment.
Further, it's arguably part of the culture to clean your trash. This is probably because burnables are collected twice a week, unburnables once a week, recyclables once a week, and, if you live in an small apartment complex, of which here are many, there is no place to put the trash. You're required to store it in your apartment until the day of collection, which means if you don't clean it it will stink up your apartment.
So, people do have time or make time.
But, I 100% agree with you that this stuff should be handled by the trash companies. They could do it much more efficiently. They can do it correctly. Having it done in a few locations is also much easier to monitor, regulate, enforce.