I think whole books could be written on "what's with the standardized tests". (and probably have been) As a subset of "What's with wanting to measure _everything_ quantitatively and make evaluations based only on quantitative measures, in our society in general?" For various reasons people wanted an "objective" and numeric way to measure student learning and compare it nationally, so they had to create more things to measure...
But it's not generally the parents that are pushing them. Except maybe to the extent that parents want to know "How do I know if a school is good or terrible?" and someone can give them a "score" built in part on standardized tests...
I think (and this may not be a popular theory), it is in large part a disfunctional reaction to the extreme social inequality in the U.S.. Going back to the days of legal segregation, some people had _terrible_ schools others had good schools. Even once we have legal equality, somehow some schools are still pretty terrible. If only we had an 'objective' way to determine which schools are effectively teaching, and reward those doing well and punish those doing poorly...
In fact, though, it's still the poor and not white who bear the brunt of all this terribleness. I know someone who is a teacher who was at a meeting where the principal was explaining why it was "only fair" to the poor students to have every minute of the day regimented and disciplined, because they too deserved the best education... while knowing the principal sent her OWN kids to a "sudbury school"!