I have to say that this is a case of "been there done that" with not only "take off" but others as well, not only with students, teachers, but also in discussion with teachers, linguistics, and so on - and learnt of this from doing university course work and so on in descriptive, historical, and so on linguistics with various lecturers/professors of that ilk, a well as reading varius articles and so on of all complexions. In other words, what you are suggesting is not the case. Of course "take" is "take off" is a "reflexive" - only in the sense that the doer is doing the action to itself - the bird took off, the dog took off, etc., it is clear that the doer is "taking itself off". The structure is intransitive, as English does not have a morphemic class of intransitive-reflexive verbs.