WebSockets is a simpler protocol built from the ground up for bidirectional communication. It provides a lot more control over the flow of data as everything passes over a single connection which has a single lifecycle. It makes it a lot easier to manage state and to recover cleanly from a lost connection when you only have one logical connection. It makes it easier to process messages in a specific order and to do serial processing of messages. Having just one connection also greatly simplifies things in terms of authentication and access control.
I considered the possibility of switching the transport to HTTP2 for https://socketcluster.io/ years ago, but it's a fundamentally more complex protocol which adds unnecessary overheads and introduces new security challenges so it wasn't worth it.