Because you can do things stateless HTML alone cannot do.
No one is trying to re-implement HTTP, or even remove it from the equation.
What people are trying to reimplement (or rather, replace) is the HTML + JSON:API + React + Redux mess. Websockets is a means to that end.
Unfortunately, great intentions alone won’t make this work; someone has to actually answer the hard questions about how it’s going to work too.
All the answers I’ve seen so far trying to answer them have been vague hand waving...
That doesn’t leave me with much confidence.
Here is the documentation for Phoenix channel authentication (what Phoenix Live View is built upon): https://hexdocs.pm/phoenix/channels.html#using-token-authent...
Additionally, here is some documentation on the security considerations specific to Live View: https://hexdocs.pm/phoenix_live_view/security-model.html
Searching can probably find you more information.
People did better than that, they already built applications with this model.