Let's take this question serious for a moment.
Modern X applications render bitmaps which get shipped over the compositor and the X server to the graphics card driver. That is not a good model for the web, because it would mean the web server has to produce rendered bitmaps, specific for the fonts, window size, and display panel led configuration over the web. The browser cannot even select text or provide a search dialog. That is almost VNC.
But originally, X applications didn't render bitmaps but submitted drawing calls. Sun used to use Postscript for that. So using that approach, it would be possible for the browser to select text, to scroll, to copy text, to search text etc. A clear improvement. But resizing the browser window would still need a complete re-transmission from the server.
But if the web server sends static html, css, and a fixed JS library, which is used to replace parts of the dom, the browser can do a lot more locally. And still the whole application logic resides on the server.