I don't think cost is a factor. You can get an AK platform for ~$500-700 like the ones from Century Arms, Riley Defense etc
There are pretty affordable ARs' available like PSA, BCA, S&W but for the most part, you'd have to replace parts after ~7k rounds. It's more about the modular design, ability to build from scratch using various uppers/lowers/butt stocks etc makes Americans gravitate towards ARs'
AKs' are good in terms of cost, usage in rugged terrain & harsh environments along with the reliability but there are certain ARs' which are on par with much better ergonomics