You want centralized sorting anyway, because a waste processor:

a) can't trust that you'll do your sorting perfectly, and won't occasionally throw e.g. glass into metals bin out of hurry, carelessness, spite, or while drunk. And even if you are perfect, your neighbour isn't.

b) might want to change the segregation rules to better optimize recycling process; you don't want to force an entire city to update their bins and/or habits in lockstep with whatever the waste processor does.

Point a) means they have to sort themselves anyway, at which point individuals doing the sorting is just wasted effort.