I am all for paying my fair share for this service.  The problem however is the management of this. Is garbage service now optional for each homeowner?  Will garbage trucks know which houses to pick up from and which not to?  Can you see the problems that will occur with people who don't have service dumping their trash in neighbor's cans or what ever public/private dumpster or can they can find?   What is the charge for a condo, $10 for hundreds of units?  If someone is renting a house, do they pay the $10 or the owner and what if the owner forgets to pay? 
In the end the cost of tracking, monitoring, enforcing this and resolving problems due to this might end up costing more than what is collecting and ending in a net loss and increase bureaucracy to pay for it.