Why do we assume this:

What we have to understand is that the US cannot win a COIN fight unless the US is the nation directly threatened. Only the indigenous people can win their COIN fight. The US can only provide external support to the government and its security forces. The US cannot win the COIN fight in any country other than our own.
Look back on US history of COIN, at least in countries where the government had either collapsed or been overthrown: so, Philippines 1899, Cuba, Dominican Republic, Nicaragua, Haiti, all in the 1910s/1920s/1930s, and even cases of just general violence (1990s Haiti and Somalia)etc., in nearly every case but one we operated under this assumption: go in, set up a government for "legitimacy," create some kind of indigenous force with the intention of turning over the COIN operation to them. As such, more attention was placed on training than on actual COIN operations. The result of this was the US started taking heavy casualties, political will disappeared in the US and the president was eventually pressured to remove troops. Then, the indigenous forces were usually not able to defeat the insurgency, and the government usually fell within a period of years: either to the insurgents or to its own security forces. In only one of those cases did the indigenous force defeat the insurgents: Nicaragua. But that was only because Somoza, head of the police, had Sandino captured and killed when he was in the capital at the invitation of the government, who had guaranteed safe passage. While the insurgency was defeated, it was hardly the kind of uccess story for US training of a professional security force that we were looking for. Somoza went on to overthrow the government two years later.

It is no surprise that the clearest COIN victory in US history (where no legitimate government existed - so I'm not talking El Salvador, Colombia, etc here) was in the Philippines in 1899 - our first real experience in full-scale COIN. The US didn't set up a government or spend its time creating and training security forces. It established a joint military/civilian government (the civ side led by future Pres. Taft), while most of the military focused on fighting the insurgency. We had support of some local forces, such as the Macabebe Scouts, and obviously that was very helpful - particularly in capturing Aguinaldo, the insurgent leader. But we didn't have to spend our time training them, as they came from a deep-rooted military culture and were already formidable fighters - and had been fighting against Spanish colonial rule for years.

Obviously it's not as easy today to just set up a military government that lasts for years, but I don't understand this rigid commitment to training and assisting indigenous forces as the only way to fight COIN. It's worked for us to varying degrees in COIN operations where a legitimate government and established army/national police force already existed, such as El Salvador and Colombia. But operations like Iraq/Afghanistan are (and potential future operations will be) quite different. Our experience in the first four decades of the twentieth century provide better historical examples.