I think that's a bad idea, simply because I don't like writing people off... which is what you're suggesting. You can take those people, and try to put them off on people who can handle them, which isn't really fair to the good people. Or you can take them and try to rotate them around, so they don't drag any one person down too much.
Or, yes, you can write them off. Shrug.
Confession: It does an Immortal Body good.
The teacher isn't writing the student off; it's the other way around. If the student doesn't wish to learn, it's not really the teacher's job to make them want to learn.
More realistically, however, the educational system has made learning an extremely unpleasant thing. Most students find it extremely painful to actually pay attention to school, and the employees are slowly facing the fact, by making the grading easier and by encouraging "social" aspects of school (I honestly had my high school guidance counselor tell me that most students didn't look back at school as a learning experience, but as a social experience. I remember thinking, "So *that's* why all these people are so f**ked up! They think this is what real life is like!").
The social aspect of school is the social aspect of a prison. There are a bunch of humorless assholes to keep you in line, a few people worth talking to here and there, you don't know who you can trust, and you don't know what will get you in trouble the next day.
The only reason the educational system stays the way it is is that nobody can agree on a better alternative, and by the time the people who could be useful, functional members of society, they've been mentally bludgeoned into being useless, sheeplike breeders of society.
You are what you think.
The problem with that approach is that when paired with a similarly disinterested partner, the two may agree that they are boredand then seek to relieve that boredom by acting out.