I think the step after that would be streaming websites. Zero code runs on the client side, everything happens on the server. All the server sends back is a visual feed / pixels. Much like the cloud gaming service Google Stadia where the game is rendered at the server and send back to the user. This might be a bit too far fetched today, but I'm sure it will happen eventually.
Pros: It will resolve many issues like compatibility and performance. Also you no longer have to wait until the browsers add new feature supports, you can make them yourself. You can use ANY language your server supports. Doesn't even have to be HTML. Websites will no longer be constrained to traditional scroll-the-text-and-pictures. The possibilities are truly endless.
Cons: It will probably use up more bandwidth (or not) and users will no longer be able to block ads (this could be a pro for the site owners though).
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