The dance organizer only supervises the DJ.
Around here, the DJ often IS the organizer... and a teacher. Not always.. sometimes they can get other people interested in DJ'ing, and even when they can't, they usually have the playlist set, so that anyone can push the buttons. Then they can at least dance every now and then.
I have known teachers who didn't dance with students. In a very small community with only one main teacher (as this community used to be many years ago) I can see that the teacher might not want to even start down that road. If he dances with one student, he has to dance with all of them or there'll be complaints and problems. Suddenly his or her whole tango experience is now about dancing with people who are not satisfactory partners on his level, in class or at social dances.
However, it still causes problems even if the teacher doesn't pick and choose from among his students, and I remember people complaining about the teacher who never danced with any of them, only with his friends who came from out of town to a milonga. So it's a tough spot to be in either way.
The situation here has changed considerably since then and now there are more teachers and more variety of approaches. Dancers travel around the region to milongas rather than only going to the one "at home". The original teacher left, and long term students became teachers. There are both male and female teachers and many guest artists who come to the region. It is less noticeable when a teacher has an annoying "policy" because it's "mixed up" more now. And of course, being the DJ is a much more "legitimate" way to avoid dancing than simply being standoffish or snobby.
My personal pet peeve is guest teachers who give workshops and privates at least once or twice here every year, know everyone in the community, come to the milonga and still don't dance with anyone except what seem to be a random few. Obviously they can't dance with everyone who takes the workshop, and they probably can't spend the whole evening dancing, but I would think that they might give SOME priority to those who
consistently take privately from them on every visit. I realize that the money for a private is paying for a lesson, not a dance partner, but as someone else said, it makes good business sense to take special care of those people who are forking over significant amounts of money to work with you whenever they can.
It's especially galling when the teacher mentions the milonga during the lesson, asking if you will be there, and implying (or outright saying) that he will dance with you.... and then never does. Ever. I've even had a teacher who diod that TALK to me for an entire tanda without asking me to dance at all!
I've known teachers who dance
primarily with their students, teachers who give priority to
private students, teachers who don't dance with anyone, teachers who dance with
potential students, teachers who dance only with personal friends, teachers who dance with only other really good dancers regardless of student/friend status, and teachers who don't dance much because they DJ. I've known female guest teachers who will dance with students who ask them, although only a brave few do. I've seen pretty much every possible approach.
My personal approach is that I always dance with anyone who takes lessons from me, but since so few do, that's not a big deal. Other than that, I don't worry about it anymore. Personal finances have prevented me from continuing to take lessons from the visitor who always says he'll dance with me but never does, so my disenchantment with him is solved already.
I DO think it makes sense for organizers or teachers to help ease beginners into the scene by whatever means works. For some people that DOESN"T mean dancing with them. I've known students who were too nervous to dance with the teacher, or felt bad for taking the teacher's time in a milonga when s/he could be dancing with "someone good". Yes, I have seen people turn down a request from their teacher because they don't feel ready!
I also think when people see the "major players" givng attention to new people or beginner dancers, the attitude spreads and that's good for the community. Maybe in very large cities like NY or London, it makes little difference. In a smaller community like the majority of the USA dance communities, the attitude set by someone highly visable is contagious and important.