There are more applications than a browser that can be exploited. Seems to me a secure GUI server is better than hardening thousands of applications.
I also prefer running trusted code, but that's not an option most of the time (for varying definitions of trust)
99% of the apps I use have no business with the contents of other apps I run so why allow it? Because X11 can't do anything about it is not a valid reason.
Browsers already have multiple layers of sandboxes. You can always add another one to the browser if you are paranoid.
Personally I prefer not running untrusted javascript in the first place (where I can avoid it). An exploit that gains control of the browser is already a doomsday scenario if you are using the browser for internet banking, work or anything that matters. Being able to grab the input and output of other applications is a nothingburger in comparison.
> Or under the threat model of company policy or legislation not allowing you to handle confidential information on a system that can't offer even a basic guarantee of privacy.
Those are usually fine with running countless proprietary drivers and tools with root access. So in other words it's security threater.