X was so "ahead of its time" that its entire architecture was dumped in version 10 to give way to X11, and then it remained so far ahead of its time that to this day NextOS, MacOS, Android and Windows have yet to adopt a single thing from it, contrary to the rest of Unix most of which has made its way into those operating systems.
Mac OS X, Android and Windows are consumer operating systems, for which eye-candy UIs are considered more important than network transparency. Their remote connectivity needs are limited to accessing corporate Web, cloud, and IT services, not other peers on the network.
NeXT was a great OS that used Display Postscript as the rendering engine, but it was also wrapped in a networked desktop environment, NextStep, and used with X11 and NeWS as well (Sun's Network Extensible Window System). I did find NextStep and NeWS superior to X11 and it's a damn shame they didn't succeed (although NextStep evolved into OS X, and Applie did include a rootless X11 implementation with it until Mountain Lion).
As for other companies, there were entire industry consortiums dedicated to expanding X and Unix, such as X/Open and the Open Software Foundation: these included companies like AT&T, DEC, Unisys, Hewlett-Packard, IBM, Sun, Prime, and Apollo.
And no, it was not designed to access resources from the desktop. It was mainly designed so that you could use a dumb terminal to access your server. When it became clear that was pie on the sky, instead of redesigning the turd, they just added layer upon layer of cruft, so you ended up with a dumb as doornails protocol running on a heavy weight, expensive "dumb" terminal.
The dumb terminal at that time was a VT100. X was designed to run on bitmapped displays. Although there were such bitmapped terminals available at the time, X mostly ran on engineering workstations. You didn't usually use it access a server (although you could); rather, other networked peers used it to display a UI on your local X display. I'm not sure why you think that is "pie in the sky" since it worked and continues to work rather well. Part of the reason for that was because the protocol was rich enough to transmit graphics primitives at a higher level than a bitmap. Nothing dumb about it.
Lastly the web browser has nothing to do with Unix. It is platform independent. The fact that you think the web==unix shows how little you know about deep OS architecture.
Don't be silly, I'm not conflating the Web with Unix. Sure, web browsers are supported by most computing platforms. But the web browser's roots in Unix go way back to NextStep and the beginnings of the Internet, at that time mostly Unix-based, and the web browser remains a central and crucial component of desktop Linux. My main point was that cleaning up web browser architecture would be vastly more useful and relevant than replacing a stable and functional part of Linux with something that is less useful, but prettier.