Per state is the key here, If we were able to compare a highly paid (relatively to COL) teacher school to a lower paid one it would be obvious if it is helpful to pay more. We need a large enough sample size of schools on both sides of the spectrum and a single state won't provide enough data or enough variance.

Perhaps, but the per state thing has nothing to do with teachers unions opposition to standardized testing and everything to do with sentiment against federal substantive standards in education, which is strongest among opponents of teachers unions.