> the biggest problem is that the DOM was built for documents, not apps

I don't see the difference. They're both text and graphics laid out in a variable-sized nested containers.

And apps today make use all the same fancy stuff documents do. Fonts, vector icons, graphics, rounded corners, multilingual text including RTL, drop shadows, layers, transparency, and so forth.

Maybe you think they shouldn't. But they do. Of all the problems with apps in web pages, the DOM feels like the least of it.