I don't even think it's an advantage to application developers. Some of the ideas behind application-filesystems have been discredited (for some of the same reasons as RPC was discredited), but more than that, it's just not that much more convenient for the application developer.
In every programming environment I can think of, you're only ever a library call away from FTP anyways.
I think it is an advantage to application developers. A lot of good ideas die because the programmer has to write 900 lines of cruft wrapper code to experiment with a 100 line cool idea, and the programmer never makes it through the 900 lines.
If you can mount web pages as a file system, then you can write a web search indexer in a few tiny lines of code. In fact, you can focus on making simply index-search functionality, and ignore whether it is a web search engine or desktop search engine.
Alternatively, you can use curl or some other library, and you can still get the job done. But you end up thinking a lot more about interface stuff to write applications, and computers end up having huge amounts of duplicate code on them -- curl, the code in various browsers, just numerous different implementations of client http all over the place, and many of them incomplete or buggy.
In every programming environment I can think of, you're only ever a library call away from FTP anyways.