You are seriously overestimating the needed throughput in practice. 60fps 1080p can be streamed with good quality over 16Mbps channel (2MB/s). The real problem is lack of good open source software that will eliminate the annoying latency due to desktop protocols (Xorg...). There are things such as SPICE or X2GO or RDP which are "OK" but I suspect much better experience is possible. The computers are extremely fast already but our software is so bad we can't see it.
Images can be compressed when using devdraw. The compression formats are relatively primitive, but they're good enough in practice. Slotting in better ones seems like it should be straightforward, though video codecs don't fit cleanly.
But once you introduce a piece of software into the middle to make this usable, what's the actual difference between this and just using VNC?
At that point it doesn't really matter if the screen is a file or not -- you need a compressor that can easily provide the output on a network socket, and a client that can perform the decoding.
You're right that it doesn't matter if it's a file or not per se.
What matters - and what the file interface gets you, but you can do the same thing in many other ways - is introducing the concept of a generic pluggable, chainable API.