A flat model like phpBB is very poor when discussions take many diverging paths, as they do here in PM. A flat model would provide no context. Ever notice how boards that use the flat model have posts that quote its parent, grandparent, great-grandparent and great-great-grandparent? A threaded model eliminates this need and the confusion. A flat model would stiffle conversation here on PM.
Use of the threaded model is hardly "ancient". I quickly came up with http://www.livejournal.com/, http://www.slashdot.org/ and http://www.kuro5hin.org/ as modern examples of threaded forums.
If you're refering to some other aesthetic aspect, you'll have to be more specific.