I think that's more a libraries thing that a language thing. For example, you can do very cool, HTMLy things using Racket's web-server/servlet and Scheme continuations, which would be incredibly hard to do in C.
But I agree with your suggestion that C should be teached first. If anything, because C's "computational model" is very simple: you know what executes when; it encourages a more common, procedural way of thinking, and it's easy to do side effects in single-threaded C.
IMO what you call the "computational model" of Scheme is also a poor fit for beginning web programmers. The most straightforward model is exemplified by PHP: put a file on the server, type its path into a browser, get the page. Change the code, refresh the page. I'm not defending the language design choices PHP made, but it nailed rapid development and deployment. Every environment that requires a recompile or restart feels like a huge step backward in comparison. I want to see my changes instantly, dammit, we had it in 1995, why can't we have it now? :-)
You can do it in Lisp... even in a long-polling application you can change a class definition and all instances are immediately updated without restarting the image or anything.
But I agree with your suggestion that C should be teached first. If anything, because C's "computational model" is very simple: you know what executes when; it encourages a more common, procedural way of thinking, and it's easy to do side effects in single-threaded C.