Re: teachers can no longer study?
If it's your class, you can do what you want...
If I'm teaching beginners, I make sure to take ukemi for as many people as possible: one of the things that makes being a beginner so hard, IMO, is working with other beginners all the time.
If I'm teaching a more advanced class, I feel more comfortable leaving them to their own devices while I train, and so I'll be sure to work with as many of the senior people there as I can.
It is challenging, though. This is one reason why I am very happy to *not* have my own dojo: I teach regular classes, but there are lots of other people teaching as well.