If you wanted to use an innovative system to redo the web from the ground up, good luck, as you'd have to reinvent this entire ecosystem to get to a reasonable equivalence
JS, Ruby, PHP, Rails, Docker, AWS, Redis, and Kafka are solidly in that wheelhouse (though, to be fair, JS, Ruby, and PHP did exist in 02000, Pike just didn't know they were important). Some of them couldn't have been built with the base OS primitives common in 02000: Docker requires cgroups, for example, and AWS requires virtualization or (originally) paravirtualization. Paravirtualization came out of Keir Fraser's doctoral research.
You don't have to write a system that has no connection to the existing ecosystem in order to be doing systems software research, or even relevant systems software research.
Also though the Web has been pretty much redone from the ground up since 02000.
Rather: An insane uncontrolled growth of extensions appeared since 2000. The only in my opinion serious attempt to redo the web from ground up that existed in this timeframe was XHTML 2.0 (https://en.wikipedia.org/w/index.php?title=XHTML&oldid=11002...). Since the arrival of HTML5 (which was a "let's standardize the wild zoo of extensions that already exist at least a little bit instead of redoing things from ground up in an organized way") XHTML 2.0 is dead.
In particular, in this context, the browser went from being a user-agent for browsing hypertext (a regular application, if one a bit 3270-like as Pike points out in the talk) to being mainly an execution environment for third-party software. That is, it became "the things that connect programs together". Most new software is developed for this platform, and it's a platform that barely existed in a recognizable form at the time he wrote the talk.