Most people try bleach first. It makes sense — pour something harsh down the drain, kill whatever’s in there. The problem is that bleach is a thin liquid. It passes over a cockroach in seconds, doesn’t penetrate their exoskeleton effectively, and drains away before it can do anything meaningful. Worse, it corrodes metal pipes and degrades rubber gaskets over time, which can create new problems.
Boiling water has the same limitation. It might affect roaches sitting right at the drain surface, but it can’t reach the sewer-level populations where American cockroaches actually live. And depending on your pipe material, it can cause damage.
The reason these methods feel like they work occasionally is that they temporarily disrupt activity near the drain. But the roaches are coming from the city’s sewer system — a network that runs under every block in New York City. You’re not going to flush them out from above. The entry point has to be treated directly, and the structural cause has to be addressed.