Although 16x16 is a little on the small side even for desktop. The point isn't just to click it, but to have it be prominent enough to see and notice as a primary action. It's about visibility, not touch area.
For example, on the SquareSpace homepage (an example someone else brought up) it's 30x18. That seems like a nice size to me. It's two pixels taller than the 16 you suggest, but the extra width helps make it a little more prominent. Especially since the width isn't taking away from anything else.