It's true that in my years taking cello lessons, improvisation never came up. That might help, but I'm not convinced that it's a complete explanation for the disconnect between me and Johann.
I confess I don't know the rules of baroque improvisation, but the links posted in other comments here seem to be faithful to the score (at least, for the ones I'm familiar with), yet the commenters seem skeptical anyone could dislike these recordings.
It's so fascinating to me that we've fallen under the very real illusion in these modern times that "classical" music has virtually no concept of improvisation, that most of the primary elements of music are completely fixed, static, dead. That's definitely not how it used to be.