Yes, one could say that the Web has "jumped the shark" sometimes after 1997 (took some years), remember the mess when Flash and Java applets were everywhere ? (WebAssembly might be more sleek, but the issue is likely to be the same...)
I guess that multimedia could be part of the Web, but support for basic features like audio/video search is (still!) sorely lacking... (Though I'm pretty sure that the capability has been here for more than a decade.)
With the ability to run arbitrary code comes the loss of a common standard, and therefore the inability to communicate, especially for machines - you might have noticed that you hardly see search engines pulling up results for supposedly "Web"Sites like Facebook or Discord or Twitter ?