Earlier quoted context omitted.
That last point is far worse than you think. In my school the principal is entirely enamored with all things apple and google and wants to mandate certain staff have twitter accounts. This is unwittingly signing up lots of people for life long tracking. Although, many already do it to themselves with no thought whatsoever to what the repercussions are, or that there may even be any. Many other schools are even worse.
Tin foil hats a side, I assume it would be an account used only for professional reasons, allowing students to reach out to their teachers. However, if the teacher is incapable of separating personal life from work, there could be repercussions.
We already have that. It's called email.