Most of the cool/useful/nice web stuff is from 
    the Ajax/fast JS/jQuery etc era of late

Wikipedia, Blogger, Flickr, a bazillion forums on which I spent countless hours. Ajax/JS/jQuery are cool, however when it comes to usefulness many times they are superfluous. The old Twitter interface was a lot more usable.

    web development is seldom CPU/Memory-bound

This is only an impression because the hard work gets done by the database or other external processes that are outside of your web server. Business logic is cheap if you can delegate the actual data processing and when you delegate, of course it's going to be I/O bound. On the whole if you count every component, web applications are the biggest consumers of these resources.

    nothing stops you writing plain apps for mobile that 
    just do the same stuff you did on the web

I agree, you can also have a native mobile interface, while the whole logic is done on server. Like in the case of a chess game, you could have the minimax algorithm (or whatever) on the server, with a push mechanism to notify the client when the move is ready.