...and no, it's not because of potential political impact on its goals. Although that's also a thing.
The Politics problem is, at its root, about forming a workable set of rules by which society can operate, which society can agree with.
The Friendliness Problem is, at its root, about forming a workable set of values which are acceptable to society.
Politics as a process (I will use "politics" to refer to the process of politics henceforth) doesn't generate values; they're strictly an input, by which the values of society are converted into rules which are intended to maximize them. While this is true, it is value agnostic; it doesn't care what the values are, or where they come from. Which is to say, provided you solve the Friendliness Problem, it provides a valuable input into politics.
Politics is also an intelligence. Not in the "self aware" sense, or even in the "capable of making good judgments" sense, but in the sense of an optimization process. We're each nodes in this alien intelligence, and we form what looks, to me, suspiciously like a neural network.
The Friendliness Problem is equally applicable to Politics as it is to any other intelligence. Indeed, provided we can provably solve the Friendliness Problem, we should be capable of creating Friendly Politics. Friendliness should, in principle, be equally applicable to both. Now, there are some issues with this - politics is composed of unpredictable hardware, namely, people. And it may be that the neural architecture is fundamentally incompatible with Friendliness. But that is discussing the -output- of the process. Friendliness is first an input, before it can be an output.
More, we already have various political formations, and can assess their Friendliness levels, merely in terms of the values that went -into- them.
Which is where I think politics offers a pretty strong hint to the possibility that the Friendliness Problem has no resolution:
We can't agree on which political formations are more Friendly. That's what "Politics is the Mindkiller" is all about; our inability to come to an agreement on political matters. It's not merely a matter of the rules - which is to say, it's not a matter of the output: We can't even come to an agreement about which values should be used to form the rules.
This is why I think political discussion is valuable here, incidentally. Less Wrong, by and large, has been avoiding the hard problem of Friendliness, by labeling its primary functional outlet in reality as a mindkiller, not to be discussed.
Either we can agree on what constitutes Friendly Politics, or not. If we can't, I don't see much hope of arriving at a Friendliness solution more broadly. Friendly to -whom- becomes the question, if it was ever anything else. Which suggests a division in types of Friendliness; Strong Friendliness, which is a fully generalized set of human values, and acceptable to just about everyone; and Weak Friendliness, which isn't fully generalized, and perhaps acceptable merely to a plurality. Weak Friendliness survives the political question. I do not see that Strong Friendliness can.
(Exemplified: When I imagine a Friendly AI, I imagine a hands-off benefactor who permits people to do anything they wish to which won't result in harm to others. Why, look, a libertarian/libertine dictator. Does anybody envisage a Friendly AI which doesn't correspond more or less directly with their own political beliefs?)