The most typographical thing is stability. Look at a book. It is visually stable. The text is where the printer has put it and does not move. You can find quotes if you roughly remember where on the page they were.
Now look at a typical web page. It is scrolled! Nothing is stable. On every move everything changes. There is not a single visually fixed anchor aside from the browser window itself, which is unhelpful anyway. (E.g. with all that talk about semantic HTML it could maybe give us a standard table of contents, but does it?) With such a drastic departure from the essence of typography some fancy hanging punctuation won't help. Of course, once the main things are in place, it would be nice to have typographical niceties as well.
Now look at a typical web page. It is scrolled! Nothing is stable. On every move everything changes. There is not a single visually fixed anchor aside from the browser window itself, which is unhelpful anyway. (E.g. with all that talk about semantic HTML it could maybe give us a standard table of contents, but does it?) With such a drastic departure from the essence of typography some fancy hanging punctuation won't help. Of course, once the main things are in place, it would be nice to have typographical niceties as well.