My intuition is from FSA to YPG, US was looking for a proxy to achieve its own goals in Syria. It is not interested in helping the PKK win against Turkey at all, instead has been hindering the PKK for decades. It does not aid PKK in Northern Iraq at all.
It indirectly supports the PKK by supporting the SDF, but makes efforts to curb PKK influence. Their current strategy is promoting the arab components of the SDF. The YPG do diffuse support with the PKK and YPG is led by former PKK. That is why the Americans have been trying hard with the Barzani talks, because they want to secure this entity in North East Syria and remove PKK where they can. The idealogy stuff does not bother them. Barzani to North East Syria is a good base for containing Iran and with Barzani in control, limits any threat to Turkey.
AKP/MHP do not like this plan. Both for domestic politics, but also because of the developing idealogy stuff, which I think is the real threat. There are millions of Kurds across the border that perceive Turkey negatively and now learn in Kurdish from school to university. They are sympathetic to Kurdish movements. America is not supporting this idealogy, they are there for their logistics and containing Iran, preventing Assad from having the oil. They do not care which proxy is capable of doing so, which is why they started with the FSA first before turning to the YPG. FSA collapsed, split into groups that joined with YPG and groups that went over to be sponsored by Turkey. SDF and SNA formed.
Turkey does not care about the small arms, PKK is hopelessly outmatched no matter how many AK's they take. But idealogically, this is the threat. Because logistics and support. America could do anything to ensure the security of Turkey and here I think there would still be an issue. Because these people exist. It's not just the Ocalan posters. America is not about to start anti-Ocalan camps now with their proxy, the same way we are not strictly vetting the SNA. We have these SNA as retainers because it geopolitically benefits us, but we do not support their cause. Erdogan does not care about beating Assad, only keeping the refugees at bay and dismantling the SDF, because of this idealogy. Since the SNA has been formed they have been prevented from taking ground from Assad and focussed on the SDF.
I think if America supported the PKK against Turkey, they could just delist them and that would be the biggest catastrophe. But no, they undermine them where they can. Syria and Iraq are a huge black market for weapons, this is not exactly something they can control. My complaint is, there is this huge perception that west actively sponsors PKK against Turkey, which I can agree with indirectly. But directly ? Russia and the East have always been the biggest sponsors. Yet they receive so much better coverage in this regard, while relations with America only recently decreased to the point where information sharing stopped as well.
Regarding Membic, America does not trust Turkey or what plans are with the areas it has. Secondly, Russia is also in Membic. America thinks Turkey is working with Russia and if they withdraw Russia and Turkey will take it. Like it is complicated. I imagine if there was a better relationship with trust, America would have wanted Turkey directly in the fight from the start.
One to watch is China, they are establishing themselves with Barzani and I wonder how they will be with the PKK.