You have it backwards, stuff like Websockets are built by design to be incompatible with existing implementations. This is because Javascript code is untrusted/untrustworthy, and we already had a plethora of attacks due to foreign JS doing nasty things with what little they had, here's a couple examples:
> Web extensions should allow you to do normal sockets
Not since 2017 or whenever it was that Firefox dropped XUL extensions and replaced them with WebExtensions. The legacy XUL extensions could do much, much more and there was correspondingly much, much more malware in browser extensions.
- SMTP/IRC spamming using Web requests (Cross-protocol scripting, 2002) - https://www.eyeonsecurity.org/papers/Extended%20HTML%20Form%...
- Webpages that detect your router and leak your SSID (or worse) - Samy Kamkar "How I met your girlfriend" (2010), excerpt: https://www.youtube.com/watch?v=tRJMIMBVqFI
Web extensions should allow you to do normal sockets, many years ago I had a Chrome app (I still miss them) as my IRC client.