I was able to use touch ID for App Store purchases before I updated to iOS 7.0.1... After that update the AppStore never prompted me to use touch ID for purchases and I would have to type in my password. The update to iOS 7.0.1 did the opposite for me of what it was supposed to fix for everyone else.
So far, I've tried:a complete restore, setting it up as a brand new iPhone, signing out of my iTunes account and signing back on, and using another iTunes account (re-doing my finger print and settings each time). I even put my iPhone on DFU (Device Firmware Update) mode, deleted the iOS 7.0.1 firmware file on my computer to force a brand new download, and had it reinstalled on my iPhone.. Only to have the same problem still.
I visited the "Genius Bar" and they could only offer a replacement (which I haven't done yet).