This is actually just a building code issue. In other cities, ordinances mandate trash rooms or trash chutes for mulitfamily buildings to avoid these issues. One could argue "but nyc grew before sane building codes," but so did boston, or chicago, and plenty of other denser cities that don't have this issue because they have sensible ordinances in place regarding waste management.
I'm willing to bet landlords don't want to make these investments to their properties in nyc, and have more of a voice in local government than their tenants, who are probably mostly indifferent about the issue at this point anyhow.
I love Boston and will vouch for the general idea that MA is better than NY, but I’m pretty sure Boston just gets by using the advantage of a smaller population and less density in this case. Although maybe the rats have as much trouble navigating as every other visitor…
Buildings have trash chutes and rooms for collecting trash; the trash is held there and put out on the street before midnight and picked up the following morning 3x per week. They get fined for leaving trash out any other time.
The issue is the collection point, not the storage prior.
I'm willing to bet landlords don't want to make these investments to their properties in nyc, and have more of a voice in local government than their tenants, who are probably mostly indifferent about the issue at this point anyhow.