Seriously, what do US policymakers have against supporting the Kurds? Are they just not aware that that's an option? I mean, I understand that the Kurds are pretty politically radical, especially in Syria, but that shouldn't prelude US support of their campaign against Da'esh. And what a campaign that has been. The peshmerga are the only military force in Iraq or Syria that have managed to consistently push back against Da'esh's advances. They won historic victories in Kobane and Sinjar, and there's something deeply satisfying about watching the empowered women of the YPJ defeating those who would see them covered and kept in the home. So why won't the US aid the Kurds?
Because they don't want to piss off the Iranians and Turks? It's not far from greater Kurdish power/autonomy to a Kurdish nation to a Pan-Kurdish nation. I'm unsure that adding another side to support in Iraq is popular in general, either.
I think you delved a little bit into it there. If the US has been consistent about one thing throughout the years, it has been its lack of support for - and even opposition toward - leftist revolutionary movements. Another factor, especially in Iraq, could be the politics of supporting the independence-minded Kurds while also pleasing the Iraqi government and the political elites that dominate it. I'm pretty ignorant about the Kurds, but from what I've read, I like them more than other rebel groups in Syria and Iraq. Edit: Also, like Quatrarius said, politics with Turkey and Iran.