Yeah, debate clubs often have many of the elements I alluded to.
Re: curation - In school settings, for example, the curation is done by the teacher (rather than the students who are actively trying to "win" the argument). Curation is needed to avoid redundancy and to ensure factuality.
Impartiality is needed in order to not alienate the parties: it undermines respect for the tool if one allows loaded keywords to be put into it. Debaters' choice of words are often "tainted" by their biases (especially if they believe in what they are defending), and there's usually a more neutral way to rephrase something someone said. More generally, though, sometimes the best arguments don't always show up at the heat of the moment, but upon offline reflection, or based on careful research.
What would be cool is something analogous to the "slowest horse" puzzle (given two people, race them to determine who has the slowest horse - the solution of which is to have them mount their opponent's horse), but in a sort of collaborative setting. I.e. people would be teamed up so as to collaboratively come up with the strongest argument against their own beliefs.