I think that depends on the audience of a forum. I'm a pretty regular poster at the SomethingAwful forums, which still utilizes a flat, quoted forum style.
Say what you want about SA, but the average poster is pretty good. We routinely carry on huge megathread discussions about a single topic with no difficulty. Just pop into any of the subforums and check it out. The Recipes subforum, for example, may have a huge megathread dedicated to Cookies. Another about Stews. Another about Chicken.
Within those, there will be all sorts of discussions, quoting, etc...but it never becomes unmanageable. You just learn to skim posts that don't interest you, read those that catch your eye, quote those that you want to respond to.
The SA forum automatically limits quoting depth, so you only see the last quote or two.
Frankly, I prefer a flat forum over threaded any day. Threaded forums are where discussions die. Once you leave the real-time, "in the moment" posting of a threaded discussion...it's impossible to spark the conversation again. Threads get too deep, there is no sense of what is new vs. old. New readers have an impossible time getting "into" the conversation, often piling into the top of a thread instead of the more active inner-parts.
With a flat forum, you just skip to the end and see what's going on, maybe browse back a few pages to catch up.
