A few days ago I wrote about how snow shoveling the public sidewalks fits well into a polycentric model. Instead of one provider of snow removal for the whole city, having each residence responsible for their own removal will best use public resources. Inevitably there are situations when residents cannot shovel, but in these events, neighbors cluster together and work out arrangements or help each other out. Using local labor saves administrative overhead of filtering the work through a bureaucracy.
What about trash removal? It feels the same. Each resident needs a service at their curbside.
There are debates across city council meetings about whether their city should take charge of trash removal or allow various sanitation services to compete for the business of each household. The former is usually desired by those who feel the extra truck traffic through the neighborhoods causes wear and tear on the roads. The latter feels that competition will keep downward pressure on pricing and allow residents to purchase the extent of service they desire.
This routine neighborhood service differs from snow removal primarily in the fact that residents can’t dispose of the garbage themselves. Nor can they assist a neighbor in the task. There is no reserve of voluntary labor tucked under the rooftops for the dispensation of Hefty bags tied at the rim. In the disposal of waste, the choices are either to purchase a private provider or take charge of it through the city offices. So a polycentric model is not useful here.

As to whether to go private or public on this one, there are benefits to both. A large city can provide many extra services such as large item removal, one-time cleanout pick-ups, that are helpful to those who don’t have means a transport for such things. Thus centralized garbage pickup with additional services is particularly beneficial in areas of a significant rental population.