A nice ideal, but likely to be very difficult in practice, because in reality almost nobody disagrees on actual provable, scientific facts. The toughest disagreements usually arise around things which are not facts, but are presented as if they were.

All human subcultures carry with them a large baggage of "facts" which the group accepts in order to promote social cohesion, avoid conflict or sometimes simply to advertise membership of the group. Try convincing a highly religious person that their religion is entirely fact-free, or that God doesn't exist using logic, and you will get nowhere: they prefer to believe things that other people don't because believing these things grants membership to a group and the benefits of that membership are perceived to outweigh the benefits of being a person of pure rationality.

Indeed, a genuine belief that you are entirely rational is simply another form of group membership signalling: probably that you want to be seen as a member of the group "intellectuals" or "scientists" or possibly "educated people". Being unable to recognise the difficulty people have in being entirely rational is itself a form of irrationality.

So to get back to your proposed social network, here's what would happen: it would very quickly become dominated by a particular pre-existing social subculture, probably "male internet geeks who believe themselves to be supremely rational" and their baggage of pseudo-facts would come along for the ride.

This is NOT an argument against doing what you want to do. Even if the goal is unattainable, creating better discussion forums with better tools for raising the level of discussion is never a bad thing. Just don't think it'd solve the 'friendship paradox' discussed in the paper.