The problem is that scaling the UI is a bit harder than scaling the 3D graphics. Scaling the 3D graphics is generally 1 line of code. Changing the UI requires planning and extra work to look good and preserve functionality at various different sizes.
Your browser example doesn't really work since most websites are smaller than your native resolution and also there are scrollbars for when things go off the page.
I can't think of any games that had this feature, and I am a game developer, so unless I am missing some obvious counter-examples, I think those points are the reason why.