But that could be done without a web-specific framework right? Say I had JavaScript on the client side send me a computation request to do something massive, say on a grid - I will probably run that using C/C++/Java there and return the result to JavaScript.

My point is, do we really need something to generate HTML at all at what we usually call the "server"-side?

"Generating HTML" on server side is done in some predictable time, while you can't make any assumptions about your users computer/OS performance thus the user experience will be random. It means problems and many lines of javascript code to solve them.