My job is similar to that of a director of studies, and in my place of work we deliver degree programmes to adult learners studying online and through blended learning. Because our faculty are SO important to our students' success it is a key part of my job to manage them. I would want to know if a student had concerns about a tutor, because our tutors' expertise is what students are paying us for, and what we pay tutors for.
I would never undermine my faulty as they are as important to us as our students, and they must obviously be treated as professionals who take responsibility for their own classes. However, ultimately it is my responsibility to ensure the students on my programmes have a good experience. Hence I want to know if things aren't going well. I'd be grateful to a student for drawing problems to my attention instead of simply leaving the course and not returning, or worse, bad mouthing the College and perhaps putting others off studying with us.
Therefore I think you are absolutely correct to have written the letter, and I'll be keen to know the response.