You're not wrong, but that's only because people wrote extensions for direct access to the graphics hardware... which obviously don't work remotely, and so aren't really in the spirit of X. It's great that that was possible, but OTOH it probably delayed the invention of something like Wayland for a decade+.
It's been ages since I've used X for a remote application, but I sometimes wonder how many of them actually really still work to any reasonable degree. I remember some of them working when I last tried it, albeit with abysmal performance compared to Remote desktop, for example.
