This system seems better to me as it's payed for by the people who use it and not by the people who don't.
The core problem seems not to be one of charging people for what they use; but the idea that avoiding the charges by dumping your trash will become common; such that it'll cost more to innocent parties - because who wants a trashed neighborhood/city? So they'll have to hire extra garbage men to go and pick up the dumped trash, ultimately at a higher cost and effort than simply having a 'pay a monthly fee that's hard to get out of, and they'll pick up pretty much all the garbage you want'. Next thing you know they'll have 'dumping cams' and littering stings. Oh yeah, and even as more people compost their food waste, more people feed more into their burn barrels, increasing air pollution.
Or at least that seems to be Manedwolf's view on it. I can honestly see benefits to both viewpoints. It's not really fair to somebody like me who generates a kitchen bag a week to pay the same amount as my neighbor who generates a full can(12 bags, it's a big can). If it was possible for me to get out of paying, I'd likely to take Werewolf's path.
It's also the reason that most states, rather than having a fee charged when you dispose of a tire build the fee into the purchase of tires; then disposing of tires merely consists of taking them to one of many disposal points(basically any tire dealership or junkyard).
It works in many areas, but not all. It really depends on the culture in the area - some areas per bag charging will work, some areas you'd get too much illegal dumping.