I like your example and "learning environment" vs "testing environment".
However, I am afraid that LW is attractive also for people who instead of improving their rationality want to do other things; such as e.g. winning yet another website for their political faction. Some people use the word "rationality" simply as a slogan to mean "my tribe is better than your tribe".
There were a few situations when people wrote (on their blogs) something like: "first I liked LW because they are so rational, but then I was disappointed to find out they don't fully support my political faction, which proves they are actually evil". (I am exaggerating to make a point here.) And that's the better case. The worse case is people participating on LW debates and abusing the voting system to downvote comments not beause those comments are bad from the espistemic rationality point of view, but because they were written by people who disagree (or are merely suspect to disagree) with their political tribe.
This is all fine, but what is missing for me is the reasoning behind something like "... and this is bad enough to taboo it completely and forfeit all potential benefits, instead of taking these risks" - at least if I understand you right. The potential benefits is coming up with ways to seriously improve the world. The potential risk is, if I get it right, that some people will behave irrationally and that will make some other people angry.
Idea: let's try to convince the webmaster to make a third "quarantine" tab, to the right from the...
(I hope that is the least click-baity title ever.)
Political topics elicit lower quality participation, holding the set of participants fixed. This is the thesis of "politics is the mind-killer".
Here's a separate effect: Political topics attract mind-killed participants. This can happen even when the initial participants are not mind-killed by the topic.
Since outreach is important, this could be a good thing. Raise the sanity water line! But the sea of people eager to enter political discussions is vast, and the epistemic problems can run deep. Of course not everyone needs to come perfectly prealigned with community norms, but any community will be limited in how robustly it can handle an influx of participants expecting a different set of norms. If you look at other forums, it seems to take very little overt contemporary political discussion before the whole place is swamped, and politics becomes endemic. As appealing as "LW, but with slightly more contemporary politics" sounds, it's probably not even an option. You have "LW, with politics in every thread", and "LW, with as little politics as we can manage".
That said, most of the problems are avoided by just not saying anything that patterns matches too easily to current political issues. From what I can tell, LW has always had tons of meta-political content, which doesn't seem to cause problems, as well as standard political points presented in unusual ways, and contrarian political opinions that are too marginal to raise concern. Frankly, if you have a "no politics" norm, people will still talk about politics, but to a limited degree. But if you don't even half-heartedly (or even hypocritically) discourage politics, then a open-entry site that accepts general topics will risk spiraling too far in a political direction.
As an aside, I'm not apolitical. Although some people advance a more sweeping dismissal of the importance or utility of political debate, this isn't required to justify restricting politics in certain contexts. The sort of the argument I've sketched (I don't want LW to be swamped by the worse sorts of people who can be attracted to political debate) is enough. There's no hypocrisy in not wanting politics on LW, but accepting political talk (and the warts it entails) elsewhere. Of the top of my head, Yvain is one LW affiliate who now largely writes about more politically charged topics on their own blog (SlateStarCodex), and there are some other progressive blogs in that direction. There are libertarians and right-leaning (reactionary? NRx-lbgt?) connections. I would love a grand unification as much as anyone, (of course, provided we all realize that I've been right all along), but please let's not tell the generals to bring their armies here for the negotiations.