From the perspective of a learner for whom English is not his first language, I can say that two-tense system alongside the notions of aspect, modality, and mood seems to be very logical, consistent, and by no means any difficult to grasp. At least, that is true for me. Also, I very much like the approach in which the concepts of time reference and verb form are separated.
However, I admit it might be seen as a difficult thing to explain to beginners, and so it is no wonder most teachers prefer not to risk and opt for the well-established, traditional and "easy to start with" 12-tenses system.
Yet, it might be worth the risk. In my opinion, this lays the foundation for the understanding of more advanced usage at a more advanced level, thus eliminating any potential incoherence and controversy. One of the typical examples of such a difficulty that comes to mind is the usage of the present perfect in time clauses, such as in "I will go out as soon as I have done my homework", which may cause problems for those who have been taught that the present perfect is always to do with the past. Some learners simply do not understand how "will" and "things in the past", as many of them perceive the present perfect here, could be connected in one sentence (not to mention cases where sentences such as this one are backshifted). This in turn can lead to even more confusing explanations, in which such a case is usually represented as "an exception to the rule". As a result, this may naturally pose the question as to why not just teach them the perfective aspect from the very beginning instead of struggling, every now and again, to get "another exception to the rule" across.
All of the above is just my opinion. I am not going to argue. I admit that you are teachers and, therefore, must know better, with all your experience and qualifications.