To me, the problem of charging for waste disposal is who the money goes to.
As so many here have said, it can be a confusing system.
If your goal is to maximise recycling then this is bad.
But if you give councils the ability to fine people, then they have an incentive to produce a system that is confusing, or at least not fix one that allows them to make money from people making mistakes.
If you think I'm being cynical, look at parking fines. The system is designed far more to get money than to sort out parking and congestion.
As for commercial waste, councils try to run this at a profit. They are in competition with private waste disposal.
Apart from skip hire, there is no significant market for household waste disposal because there is an adequate, free service.
If the council switches to an expensive, complex system that turns up to collect waste when it feels like it, then it's pretty easy to see a private contractor going for the money.
If I were competing with the council, I'd do stuff like give people a choice of bags or wheelie bins, not making them haul rubbish on to the street (good for older people), and chuck in a service for bug ugly stuff like old furniture.
I might even go for an upmarket greener service. Because I am a businessman, ie their servant, not their political master, I'd do stuff that made them hnappy to use me.
So for instance, each month, I'd email all my customers saying that I'm collecting stuff for a designated charity.
Electronic waste (old Pc, stereso etc, is actualy quite valuable, and at the same time rather toxic, ideal for recyling). The next month I'd collect old toys, then old clothes, you get the picture.