It's absurdly complex, and there is little guarantee that the SVG spec is implemented completely and identically in different environments. I know of several native GUI SDKs that do not support a large portion of the spec.
Even something that should be easy like doing a wireframe or mockup in Sketch, exporting to SVG, then displaying that exported SVG in a browser on the same machine can display jarring errors in the rendered image.
And most of the cool shit in SVG - like embedded JS and the filters spec - are where those issues rear their heads.
What I'm saying is that SVG is as much a shitshow as HTML. It's just HTML with additional drawing semantics anyway.
I think it could be utilized more often for simple presentational components, such as dialogue boxes or modals, or for various bezier-piece paths.