The C10k problem was originally about serving static files -- quoting the page you linked to: "take four kilobytes from the disk and send them to the network".
The demo could certainly be extended to send larger amounts of data -- left as an exercise for the reader.
I'm not sure to understand your second paragraph -- if I used this system in a real application, I would serve the pages with the traditional handler (with template rendering, middleware, etc.) and then exchange messages over the websocket. These are different roles.
Regarding database connections, the default behavior isn't the one you're describing any more; I implemented persistent connections in Django a few weeks ago.
The demo could certainly be extended to send larger amounts of data -- left as an exercise for the reader.
I'm not sure to understand your second paragraph -- if I used this system in a real application, I would serve the pages with the traditional handler (with template rendering, middleware, etc.) and then exchange messages over the websocket. These are different roles.
Regarding database connections, the default behavior isn't the one you're describing any more; I implemented persistent connections in Django a few weeks ago.