I taught high school math for 2 years. Which really isn't really enough to diagnose (much less solve) the system's problems. But it did give me a sense of how intractable the problem is.

I find it enormously frustrating when people (not you) complain about "teaching to the test." Teaching to the test is good pedagogy! First, determine what you want to students to know/do. Then choose how you're going to assess their knowledge/ability. Then design instruction that prepares them for the assessment. This is called backwards design.