Websockets address a different need than XMLHTTPRequests. The latter means that his name says: query: you know that you need something (that is, because the user clicked a link, scroll, or something else), and you get it - and XHR does an excellent job of this.
The malfunction begins when certain events can be triggered on the server server, which should be sent to the client in real time. The only thing you can do right now is to regularly test the server - this is a hack that contains many problems. And this is exactly the problem with which websites are created: Provide a browser for viewing in real time for real-time notifications.
I think Ajax XOR Websockets is a kind of false dichotomy. They affect different needs and can coexist peacefully.