It is not much further then Athens (if not a little closer) Is there more traffic to Athens then Istanbul?
A3 doesn't fly to the US AFAIK. TK reaches more destinations than any other airline IINM, has government support, and has quite a few nonstops between IST and North America, in addition to perceived instability/danger.
I think we might be more likely to see a US airline initiating a route to Moscow or Kiev than to Istanbul.