I think one must "unlearn" some of the habits created in normal life to learn piano well. One is the every day left and right hand coordination.
A bit different issue for me is, that I feel that everything I play is neglecting my left hand. My left hand is just as capable as my right but gets much less workout. So in my mind I have played with the idea that I should play the right hand parts on the left as an exercise. I have a book on pieces for left hand but haven't really had time to work on it yet.