This is called "having a conversation". In flat discussions you can't bicker endlessly because a large portion of the posts are just replying to the OP. There isn't as much back-and-forth or progression of the discussion. Discussions tend to get only a few levels deep.
The only time anybody has changed my mind has been on nested forums, like this one. It is because we had to go back and forth three or four times to arrive at a new understanding. Nesting let us track that discussion.
Maybe it's a personality flaw, but I have had far fewer enlightening experiences on flat forums!
For people who really want a conversation, I think a forum should support some way to privately contact one another. And a good ability to start new discussions. But for general-audience, broad-appeal forums, I think threads usually create more problems then they solve.
So you've replaced a perhaps over-verbose but relatively easy-to-follow set of discussions with a smaller, but much more confusing and hard-to-follow set of discussions. You might have succeeded in limiting "bickering," but I think to a much greater degree, you've reduced the quality of the discussion (to a bewildering mush in the worst cases).
So I think it's no accident that, based on my experience, flat forums usually seem to be, well .... pretty shallow (and I mean that in a bad way :)... they're fine for saying "hi!" and talking about the weather, but surely we'd sometimes like more than that?
My default now is to leave them out. There are some contexts where lots of argument is valuable, but generally it's just a strain on the social fabric without a lot of upside.