Islam only has been in existence for about 1300 years, so 2 millenia is a bit pushing it. Those regions were barely Christian for a few centuries until they became predominantly Muslim.
I almost never hear anybody advocate for a Kurdistan, so I'm not sure where the idea of a fixation comes from, but with the Kurds you have 30 million of them in a relatively confined, contiguous area that covers well-defined peripheral regions of several states. Thus it's an ideal subject for its own nation state.
Syriac Christians and Jews tend to be ancient remnant populations that live in the midst of Muslim majority areas, so it makes little sense to talk about a "Christian Syriac nation." Plus there's very few of them left. I don't know where you get this "outnumbering" concept from. There's like 2 million Assyrians total, spread everywhere across the globe. One of my wife's best friends is Syriac Christian, and there are hardly any of them.
I'm not claiming the Kurds are the most wondrous civilization known to Man, but they are the fourth largest ethnic group in Western Asia, they live in a comparatively isolated contiguous area where they are totally dominant in the population, and it makes little sense for their region to be divided up between Iraq, Iran, Syria, and Turkey. If you were drawing up a rational map of nation states in the region, based on existing populations, it's a total no-brainer.