We used to think that was a good idea. But if the person is not actually trying to argue or discuss topics in good faith, but is simply exercising their particular side’s propaganda, there is no value in them being there.

Obviously this is a grey area judgement call, but the difference is real. It is for the same reason that there is generally no point in inviting a serving politician on the panel, because they will reply to everything with their prewritten talking points, which you can get from their party’s mailout or any of the press conferences given by their frontbenchers.