Given that websockets don't even work reliably yet, and are not even implemented in all popular browsers of the day, that's hardly a proposition. Not to mention that everybody implementing his own HTTP replacement from scratch with websockets instead of a common standard is a highway to hell.
As for what's wrong with it:
- better support for non-blocking requests
- better support for streaming media
- better support for caching
- better content negotiation (e.g for "retina" x2 assets)
- better authentication mechanisms
- better support for encryption
