In 1993, I was the only person I knew with a web browser. 18 years later, we have applied hack after hack to make it into an "application platform." And it's still the same old thing.. a way to deliver hypertext pages to people.
If you want to allow people to sync their files, share large popular binaries or listen to the perfect mix of music, you don't do it over HTTP. Not because you don't understand HTTP, but because you do.
HTTP is also extensible (by design), which has lead to stuff like WebDAV and the like. Stuff that is used large scale, over the web. So the web is not 'just' HTTP.
There's deliberate trade-offs in the web's architecture which means, unfortunately, you can keep coming up with edge-case applications which are challenging (although often not impossible) to implement using web technology. The reality is that a large majority of applications are information-centric, are distributed in nature, need to evolve over extended periods of time, and therefore benefit _greatly_ from the trade-offs that the web has made.
The web's not perfect but it's evolving and - importantly - it doesn't have the benefit of being completely fictitious and living inside the mind of a jilted, chippy geek. No offense. ;)