Let's say I have a URL which points to a file on an HTTP server that is
constantly being appended to.

Could [lib]curl not efficiently poll (at a prescribed interval) that URL
looking for newly appended content using whatever mechanism is behind
the -C option? If nothing new was added it should be GET with no
content but if something new was added, the effective -C option would
only get the new content which would be sent to stdout (or a file for
-o/-O).

Is there something about HTTP that I'm missing that would make this not
work?

b.