Theoretically? No reasons other than those I've given above. But empirically it's awfully rare to do that successfully, and people have tried. About the only ones I've been happy with are written by our own Scott Alexander (of slatestarcodex), and his politics are close enough to mine that I don't totally trust my judgment there; I'm more libertarian than he is, but that's a relatively petty difference given what he tends to write about.
The more common outcome is that a writer sets out to build with steel but inadvertently builds with straw, not so much maliciously as through honest misunderstanding of the opposition, and is only confirmed by the exercise in their existing beliefs. We're very good at fooling ourselves into thinking that more or less subtle caricatures accurately represent our opponents' motives.
And I expect I'll probably catch some flak for saying so, but I don't have much faith in LW's ability to move past that stage.
One of my favourite Less Wrong articles is Politics is the mindkiller. Part of the reason that political discussion so bad is the poor incentives - if you have little chance to change the outcome, then there is little reason to strive for truth or accuracy - but a large part of the reason is our pre-political attitudes and dispositions. I don't mean to suggest that there is a neat divide; clearly, there is a reflexive relation between the incentives within political discussion and our view of the appropriate purpose and scope of politics. Nevertheless, I think it's a useful distinction to make, and so I applaud the fact that Eliezer doesn't start his essays on the subject by talking about incentives, feedback or rational irrationality - instead he starts with the fact that our approach to politics is instinctively tribal.
This brings me to Joseph Bottum's excellent recent article in The American, The Post-Protestant Ethic and Spirit of America. This charts what he sees as the tribal changes within America that have shaped current attitudes to politics. I think it's best seen in conjunction with Arnold Kling's excellent The Three Languages of Politics; while Kling talks about the political language and rhetoric of modern American political groupings, Bottum's essay is more about the social changes that have led to these kinds of language and rhetoric.
Video of a related lecture can also be found here.