I think it's a very good idea. Discussions often derail into argumentative wars of this kind. Of course, there is also the opposite failure, referred to in some of the other comments, namely that people agree too much, don't point out flaws in others' arguments for fear of upsetting them, etc. In order to resolve that, you need a different strategy, just like different biases require different counter-bias techniques. That does not establish that this strategy is not helpful to improve the kind of discussion described here (which, by the way, is very common).

The general idea of changing contexts is also very interesting. It seems to me that how discussions unfold is to an extremely high degree due to situational features. For instance, at my previous department, the discussions in the small seminar room were nearly always more cooperative and fruitful than those in the large seminar room, which felt much more official and somehow prompted people to take a more adverserial stance visavi the speaker. Probably we should change contexts more often to find out under which circumstances the discussions tend to become most fruitful.