Depends on what we mean by critical thinking, as I said it is an abused term. Some just use it as a substitute to mean "thinking for yourself" when that is not something taught in a lesson but either becomes a habit or doesn't. But even then we all use arguments from authority and present it as our own because you are not realistically going to think about everything from first principles all the time.

I agree that districts do have a lot of pressure on teachers to keep pushing up test scores which leads them to being gamed either by teachers or children no matter the tools available: https://en.wikipedia.org/wiki/Goodhart%27s_law