While I do agree that there's nuance for sure, in the case of what you're referring to it's just a lack of tooling. There's are SOME advantages (mostly in dev simplicity) to having stateless protocols such as HTTP, but the flexibility of reusing a socket can allow building much better (especially better performing) applications.

No matter what there's no case where back and forth HTTP is faster than WebSockets. The only exception would perhaps be extremely well optimized QUIC http servers with literally ideal data sizes (and even then WebTransport or WebRTC would beat QUIC)