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