Everyone probably already knows this, but enabling compression (-C) makes running remote X programs more usable over slower connections.
IIRC it's written in Python, so it runs in most places: https://xpra.org/
It's not something I know a lot about. Is this where VNC steps in?
Really? Probably half of all web servers on the Internet (using HTTP/1.1) use it.
> The proper solution is surely to use a modern lossy video-compression algorithm.
The X11 protocol doesn't send bitmaps so I'm not certain that a "lossy video-compression algorithm" is gonna have the effect you think it will.