Why more than 10 FPS is needed
The brain can process an image displayed for as little as 13 ms if the surrounding content is blank.  10 to 12 images per second is only the number of images that appear distinct to the eye.  Beyond 10 to 12 images a second,  the brain starts to try to piece them together, but it is doing a lot of work to make that go and the motion isn't as smooth as it could be.

Using higher frame rates means that the brain has to do less filling in the gaps and motion can appear more accurate and smoother since the brain is actually fully capable of processing images faster than 10 times a second.

The 12fps animation threshold is only a minimum to get the appearance of motion, not the maximum amount of information our brain can take in.  We can process far more images per second to determine motion, but require at least 10 to 12.

You can test this for yourself if you want by taking a 30 fps video and inserting a black frame at random in the video.  You'll easily notice the distortion from the missed frame because it abruptly changes to something other than the expected image.

Basically your brain knows what it expects to see and can recognize that it didn't see what it expected, it just can't recall exactly what it is that it saw that it didn't expect since it was taking a shortcut to reduce the amount of processing needed.

The Wikipedia article on frame rate is a good source of additional information on the topic.