To the author's take of using a file system as an interconnected 'web', we have networked file systems today, typically clustered though.
We've also had the _concept_ of a media-rich file system, like WinFS [as an overlay to NTFS], which was dead before it was alive due to the WWW.
Networking file systems is _complex_. All vendors would need to agree to a common export model on top of their preferred file systems. Or users would need a specialized partition/overlay developed just for this purpose.
FSes are great, but they're not fit for WWW. Without a control plane, they lack any tooling that makes the WWW better -- redirection, access control, programmatic execution of content (ASP.NET, PHP, CGI ...), etc.
Ultimately this would be a complex solution. Just like many don't simply "open up" their web server to any and all traffic to any and all content, a file system would need to be carefully partitioned the same.
The time for file systems as the vehicle for WWW content is long since past. We have better ways to do things, better caching mechanisms, better performance [through CDNs], better security mechanisms, and so on.
...not to mention, I certainly don't want to open my personal computer's file system up to the Internet.
There would have to be a big leap in evolution of file systems across all major operating systems for the author's dream to come true. I would certainly be excited to see it, but we're talking about allocating _talented_ developers to create a new file system and certainly an open source file system. Like many file systems, it would take years to become a trusted file system to host any content of value.
In the mean time, the author can always investigate WebDAV. Slower than dog shit, but it's available with every major web server.