Web was always about backwards compatibility. You should be able to contact with HTTP web server deployed in 1995 from modern web browser.
Server push is different, because it's supposed to be an invisible optimization, so it could be dropped without anyone noticing. But most things are not invisible.
> You should be able to contact with HTTP web server deployed in 1995 from modern web browser.
AFAIK, a web server deployed in 1995 would probably be using HTTP/0.9, and I think modern web browsers don't support any HTTP older than HTTP/1.0 anymore.