The generalizability theory can be used to examine the effectiveness of high school teachers. It is hard based on the fact that each student will learn in his or her own way. I think that you couls do an overall generalization to get a somewhat clear idea how well the teacher is doing but other factors will come into play.
Yes, the generalizability theory should be used to examine the effectiveness of high school teachers, because the sad truth is that high school is a cattle call. A teacher is not effective if they are only good at educating low functioning students, or athletes. It is fair to look at what the teacher does as a whole.
The generalizability theory is a way to measure performance and I believe it should be used to examine the effectiveness of all public school teachers, not just those at the high school level. I believe many teachers have gone unchecked for far too long. We need measure teacher performance in a variety of ways to get the best idea of how they are doing.
No, the generalizability theory shouldn't be used to analyze teachers because different teachers have different methods of working. For the most part the theory is great to analyze things, but teaching is not one of them. I've had both good and bad teachers that have the same characteristics. It wouldn't prove anything to look at them in a general manner.