Re: teachers can no longer study?
I think there are plenty of teachers who get to little practise themselves, and stop learning. If one is teaching the majority of one's training, one has to structure the training so one actually trains while teaching.
One way of teaching is letting all the students take ukemi for the teacher - possibly also the other way around, but if the class is big there is little time for this. The importance for students to feel and experience good techniques is often neglected, I think. I don't understand teachers who seldom lay their hand on a student in order to do technique - not primarily in order to "correct" something - other than a few favourite uke, and expect the class to truly understand what they are doing.
Physical training... well. If only throwing, not taking ukemi, you kind of remove what conditioning stuff there is in aikido. Someone who teaches this way must either do complementary fitness training or pretty soon be out of shape, IMHO.
Having that said, I think the OP will find more learning through teaching the more he teaches, even in just following his own teachers's way of teaching.