An anecdote: My NYC neighborhood has seen a building boom over the past decade. As far as I can tell, every new building puts its trash out on the street.
Some particularly memorable examples include a 75 story residential tower with absolutely record-breaking trash piles, and a ~25 story residential tower with a trash collection point on the onramp to the Williamsburg bridge. Garbage trucks have to stop in the road to collect trash, manually, bag-by-bag, at every stop.
This is the policy for trash in NYC, and rats will remain a problem as long as it stays that way.