Broken may not be the best description. People are managing to make it work just fine for the most part.
Unnecessary may be a better way to put it. What benefit do we really gain from doing all kinds of crazy DOM manipulations to return to what effectively amounts to a framebuffer and a few built-in drawing functions, emulating what we've been able to do on the raw hardware for decades?
"It exists" seems to be the best justification at this point. And that is a pretty strong justification, don't get me wrong. There is simply nothing better for on-demand distribution of network applications.
However, if we were to rebuild the model from scratch, I see no reason why we would want to include HTML as the basic building block. HTML rendering would more appropriately be an application built on top.