Of course there must have been a reason Bach would have wanted to write, it's one thing to have the Talent but there needs to be a reason for Music rather than Just the Music it's self. Perhaps they were just in harmony and could hear each others music clearly

Yes, or since she had been a student of his, from a young age, more than likely the student absorbed and made her own what she had heard & learned from the master. Individual differences, but very similar all the same.