Could you expand on what you'd gain that isn't being done already? I'm not following what you mean here.
Web developers already use SVG for complex vector illustrations + some JS or CSS to animate the SVGs, coupled with CSS for simple shapes (like circles + rounded rectangles with shadows), and CSS for responsive layouts (SVG doesn't have anything similar to CSS in terms for responsive logic or layout logic as far as I know).
This works well enough, and for example you can replicate most UIs you'd see on different platforms without getting too crazy. I feel most UIs people want to build just really are composed of mostly rectangles, oval and circle, some layering and some shadows - CSS alone is decent at this.
To address the second paragraph; I have a feeling that the limitations of HTML/css influence to a degree some of the result UI design. If you look at some stellar native UI’s, there are many little details and also more complex interactions which would be very bulky to implement in a web app, with probably prohibitively bad perf. It’s hard to think of examples, but maybe the JetBrains IDE’s, CAD tools, MS office (their online versions use almost all SVG, at least in PowerPoint).