I was gonna mention this idea, but you beat me to the punch! Nice one! I think being able to sing what we play can be more important than being able to play what we sing. Sometimes a person will attempt to learn a physical pattern as just a physical pattern, but they won't have a solid understanding of what the actual rhythmic phrase is. Therefore, they can't play it very musically, and sometimes not even accurately.
In my teaching studio, students tell me all the time that their lack of physical coordination is why they can't play a specific drum pattern. I say, "Oh really? Then, let's take your physical coordination out of the equation. SING the phrase to me. What is this thing supposed to sound like?" Nine times out of ten, they can't sing it. At this point, we put down the sticks and spend time practicing singing the rhythm. Once they can sing it, we go back to playing, and the "lack of physical coordination" problem is normally solved.