XHTML2 (now abandoned) was a serious effort in that direction (while sticking quite close to existing HTML) - consistent syntax and rules for handling it.
Honestly I don't think we'd see much change to what browsers can do - like turing-complete languages, everything is possible on the web, just not necessarily as easy as it should be. A lot of parts of the web I view as "assembly languages" - it would be possible to use better alternatives to HTML, CSS, Javascript and perhaps even HTTP, but it's not like we handle any of those directly. So no-one should care except a few library authors - and the libraries have mostly been written now.
Honestly I don't think we'd see much change to what browsers can do - like turing-complete languages, everything is possible on the web, just not necessarily as easy as it should be. A lot of parts of the web I view as "assembly languages" - it would be possible to use better alternatives to HTML, CSS, Javascript and perhaps even HTTP, but it's not like we handle any of those directly. So no-one should care except a few library authors - and the libraries have mostly been written now.