I'm going to guess you've never been there and don't have any actual knowledge of what you're talking about, as usual.
First, I'm quite certain there are a lot more carriages there than in SA. Second, while every carriage has that bag, not every carriage doesn't have its own dedicated poop scooper. I've never heard of anyone deploying them on such a large scale.
Have I been there? Yep, but I was a young kid at the time and don't remember much.
But are you seriously going to try to tell me that NYC has that many more horse carriages than SA? SA is a HUGE tourist spot. The amount of stables in and around SA has far more horses than NYC has.
There are a few carriage companies that compete downtown. My friend's wife drives for one of them. And yes, not only do all the horse carriages have bags, each carriage is followed by a dedicated pooper scooper person that picks up the occasional rare pop that misses the bag. There is literally zero poop on the streets because of that. It's not that hard to hire some workers to follow horses around for a few horse at night and make sure there isn't any poop left on the ground. Pay for those workers, like the handlers, drivers, and such is all handled in the price of the carriage ride. Depending on the carriage type and length of the ride determines the price. It can range from $30-$150 for a ride. My friend's wife pulls in on average $350+ in tips alone on Friday/Saturday nights. He said she made over a grand on Valentine's Day last Friday for about 5 hours of work.
Of course as the driver you have to sit behind that poop bag all night long....