However, between custom OpenGL UIs and HTML-based UIs, there is an entire spectrum of native apps (mobile and desktop) that make use of platform conventions and standard functionality. This space is difficult to cover with web technologies because you have to simulate the look & feel and make the site feel like an app.
Many people have tried to build "just like native" toolkits from WebGL and DOM, but it's pretty tough. WebGL is very low level for this, and DOM is much too high level for many things.
That said you seem to be far enough along that redoing the GUI would not be a good idea really.
Also the DOM is a fairly okay retained mode UI, so if that is your preference I would just use it.
IRL, we don't expect toilets, hammers, bulldozers, shotguns, and surgical scalpels to have the same user interface features, and it would suck mightily if they did. Unfortunately, as those things get computerized we wind up getting the same crappy touch-screen menus and whatnot bolted on to them (imagine what using a hammer with a touch screen interface would be like).
I don't know the answer to how it could be brought about, but we definitely need some radically thinking in UI design. 3D libraries seem to at least provide the tools to make some new tools.
You really wouldn't mind if the app used control-p for delete, and control-z to quit?