While Tim Berners-Lee was indeed mostly concerned with (scientific) documents, with form support HTML 2 already introduced application-like features. HyperCard, one of HTML's spiritual precursors also was very much about applications.

That said, I'd like one feature of the original web browser to be much more prominent (or in fact to be available at all): In-place editing and instant publication of changes, alongside with version control.

That'd of course require infrastructure for those publications to run on. So, it'd not just be a different browser UX but an entirely different way of publishing on the web.