The school district is not just about the schools. It also reflects the population in the neighborhood. Simply put, there is a correlation between the API and the income. It is very useful to get a general idea of the areas if you are new.
When you choose a school district, you are not really choose the teachers but rather the peer students.
As for test scores, if everyone is gaming for the scores, then it is a fair game. What is tested is not that important. If every student is required to be tested on Greek or Latin, the grade is still a good metrics to measure the effectiveness of the teachers and the learning behavior of the students.
