Argument mapping is a pretty well-established genre (https://en.wikipedia.org/wiki/Argument_map), and over the years there have been many software incarnations of it. I think one reason that it hasn't caught on as a way of resolving political issues is simply that many people, if not most, are not interested in rational argument. They have an objective in mind that they did not arrive at by reasoning it out, and now they want to achieve that objective. To them, argument simply gets in the way of a decision that they have already made.