I don't think TeX output looks better than what Web browsers do if you enable all the high-quality text features like hyphenation and use modern OpenType fonts (in particular not the Core Fonts for the Web). The reason why the Web doesn't do this by default is backwards compatibility and performance: hyphenation is asymptotically more expensive.
TeX doesn't hyphenate every word, it only attempts hyphenation when it looks where to break a line. That said, I don't see why a document cannot be prehyphenated once on the server; I'd say this is the right thing to do. (Besides, in this case we don't have to rely solely on algorithms.)
It's not that CSS is still very far from professional typesetting; what amazes me is that at the same time it's much more complex. Look at all these possible 'display' values and box models! And you still cannot do a run-in header! Or automatic numeration! (You can do the latter natively with XSLT, but it's not cool.) By comparison TeX only has boxes, vertical and horizontal lists, glue, and a few lesser things like kerning. And it produces works of art.
