The web works because of HTML. HTML is scanable, searchable. It's what allows search engine to exist at all. HTML enables extensions. HTML is also generally responsive. HTML allows uses to be in control (see extensions). HTML allows uses to copy and paste and even for sites that try to prevent it users can go into devtools to get the text. HTML supports all of unicode and so is inclusive across all languages.
A world in which the browser is just an executable environment and people make random UIs means pretty much all of the above disappears. No more searching for content, no more extensions to block ads or block distrdacting feature. No more extensions for language translation, braille, accesabiltiliy. No more all language support, only whatever each framework decides to support, every page with different limits at different versions of the frameworks.