It's too bad that physical coordination is assumed in traditional piano pedagogy, and even in some more holistic disciplines, like Dalcroze Eurhythmics. As a child I had terrible physical coordination: not only could I not throw a ball as other children did, but I retain memories of clumsy movements in gym class, where we swung Indian clubs - I simply couldn't do it.
What I could do was move my fingers in response to what I heard. My ear was the switch that empowered my piano playing. It still is.
When required, or expected, to respond as others did, or to imitate the teacher, I simply fell apart, dropped out. But on the sly, when no one was looking ... well, I haven't stopped.