"The technologies that could be called "the internet" solve more well defined problems than the technologies that could be called "the web"."

I'm pretty sure the original problem the web was meant to solve was the problem of enabling hyperlinks between documents that are distributed across many servers. The original concept solved this very well, scaled very well, and was then hijacked by people who thought that "document hyperlink system" means "application delivery platform."

(OK, there were a few things that happened that I glossed over, but the web's original goals were not as poorly defined as you make it seem.)