Yeah, honestly the density numbers are tough to find because "NYC" always includes Queens,etc....so you kinda have to go look at subsections of major cities.
The point is that Manhattan isn't particularly dense when compared to other world-class cities major population centers, and these other places have solved the problem of trash collection. NYC exceptionalism seems to be the fall-back explanation for why it "can't be done"....but to me it fails under further inspection....literally fails the smell test :)
Finally, you're correct that the trash bins aren't a panacea, but not allowing a literal rat buffet to fester on the sidewalks 3 nights a week is a good first step.
