I agree that webhooks have their problems, but, as somebody maintaining software that uses long-polling heavily, I will say that long-polling is quite difficult

I agree that webhooks have their problems, but, as somebody maintaining software that uses long-polling heavily, I will say that long-polling is quite difficult to handle reliably "over the internet". ISPs have very different views on how long a connection is allowed to be kept open, and will absolutely kill long-polling connections without remorse. This extends beyond ISPs, too. Practically all network infrastructure between API consumer and API will have to accommodate long TCP connections, which is unfortunately not as trivial as it sounds. The next cool feature of long-polling is that the server might not know that the connection is broken until it actually tries writing to it, so if the back-end relies on having or not having a connection, this will make for some interesting edge-cases. Load-testing products using long-polling also has interesting implications, such as hitting the "65k" problem on test clients and network infrastructure. Add another layer on top (or below, like Kubernetes, OpenShift, whatever) and you should be getting a prescription for anti-depressants from the very beginning, because you WILL need them.