This is, emphatically, not even close to true. If someone told you this, they were lying or just had no idea how schools work and were guessing.
> early school start times which help teachers at the cost of students
A perfect example of how you're veering away from reality with your faulty premise: teachers don't like super-early starts, either! Except the coaches who like having plenty of time for long after-school practices with the sun still up. Parents of athletes may like it, too, just so only one end of their daily schedule changes when their kids' sports are in season (as opposed to having to get them in for an early practice, and pick them up late for a late practice, unable to use the school bus for either end). The justification given for keeping it is usually some combo of "parents want it" (do they? I'm a parent and I fucking don't—but then I don't have any high school athletes in my house yet) and, overriding all other concerns, school sports. Adjusting those schedules may also mean elementary kids start earlier so that the high schoolers can start later, because districts want to be able to stagger bus schedules so they need fewer busses—again, not because teachers are demanding it—which I guess maybe some parents don't like (I'm a parent of elementary kids, and yeah, I'd like them there earlier and the high school kids later, reverse of how most districts do it, but maybe some parents do in fact want their elementary kids starting at 9 o'goddamn-clock when they've already burned 1-2 of their most alert hours for the day, and the high schoolers starting before 8:00, for some reason). It is absolutely not because teachers are demanding to start school before the sun's even up in the Winter.
I don't believe there is any purpose in the current school start time, but it's been this way for ages. I'm sure it works for at least some people - but I don't see any reason why student athletes couldn't practice in the morning and spare the rest of us.
-A teacher I was talking to last week
Point is, test scores aren't perfect.
That's the only power any worker has. Pay and/or other powers tend to correlate to how often the worker ceases to work and/or how expensive it would be to replace them (true for both union and non-union workers).