If I were you I probably would, although the wording could use a little work. It would probably help you guys to work through your feelings of superiority to the therapist with her, as then you would be more open to the work itself. I would open a letter like that with something like: "I'm just trying to be honest here, so you can understand where I'm coming from, and I don't want this belief I have to be an impediment to the therapeutic process. I feel like this letter might be a good place place to start - something for you to work on. What you need to work on is not to destroy your belief in your knowledge of psychology, but your measurement of how great your knowledge is.
I would also like to add here: I have friends who are therapists who also visit therapists themselves once in a while, when they need it. They are very good at what they do, and may even be better at therapy, and more knowledgable in psychology than the therapists they visit. The process itself is what makes it work; I would expect your knowledge of psychology to be a credit to your ability to improve rather than an impediment. It doesn't take a special therapist to help you, the teachings they have work great if you are willing to use them, think them, and better yet accept them. You may even find it useful to think of yourself as an especially responsive patient, a great listener and a person who is unique in their ability to take honest truths onboard. These beliefs all helped me to take onboard the advice that my therapist had for me, and to be honest I still think of myself as a special patient. I sometimes wonder whether my therapist does too. hahaha.