Taylor Swift was definitely a special artist for me. I didn't notice it back when I first learnt about her, but I did notice it as soon as early 2009, when she first became popular worldwide. There was something that made her different, although I couldn't quite pinpoint it.
Then in 2011, Amity Shlaes, writing in Bloomberg (Read here: http://www.bloomberg.com/news/2011-12-01/taylor-swift-as-counterculture-icon-for-teens-commentary-by-amity-shlaes.html), proclaimed Taylor to be a 'Counterculture Icon for Teens'. I personally think she put it quite well in that article. Most music was "anti-parent, or at least parent-free", Shlaes explained, and that "most parents have assumed there was nothing you could change about this dynamic". At that end of the article, having examined Taylor Swift's pro-family style and her popularity, Shlaes concluded that "maybe the professional entertainers held sway too long".
Taylor Swift is what a popular cultural icon should be like, to me, and to many other people. Of course, there will always be those who prefer people like Lady Gaga, Ke$ha, Rihanna and the like, but to me, it's just normal human nature to prefer someone like Taylor Swift over them.
So do I agree that Taylor Swift can be seen as a Countercultural Icon? Yes and No. What she does can seem countercultural at times, compared to the 'norm' out there. But then, it's probably because the 'norm' has been distorted. Rather than being countercultural, I suggest that Taylor Swift represents a return to what normal everyday people desire to see in their entertainment scene, taking back power from those who have too long controlled the scene and think they know what's best.