Yes, they do that. But they often use Xshm to upload those pictures to the display server, and that still means sending them to the peer for server-side blitting.

Further more, by using TCP/X11 for the wire protocol, any dropped packets have to be retransmitted before you can update unrelated portions of the display because it requires in-order processing by design.

This is why high-quality, high-frame-rate remote displays never use that design.