Responsible? Yes, along with all kinds of other entites. But all that isn't terribly relevant to my actual point, which is that the political capital that will be expended on maintaining those benefits will create openings to oppose the teacher's unions in other ways.
If you want names named, the SEIU is the biggest problem of the bunch. But it's all the same problem, unfunded defined-benefit mandates. It doesn't matter who is getting them when they exceed what society can afford.
I absolutely agree with you that our current methods of selecting, training, and critiquing teachers are deeply flawed. But they’re flawed for a whole host of reasons, and the teachers’ unions that fought against the often worse problems of the pre-union past are not by a long shot the biggest problem facing the education system.