Yeah this is mostly true. I have a large group of friends from undergrad who became teachers and most when given the opportunity chose to become administrators. And when you ask them, they eventually admit they do it because it's the path of least resistance to a slightly above average salary.
But, there are teachers who love being in the classroom and turn down the admin jobs. My homegirl had a chance to go from 60 to 80k in a admin spot but turned it down because she would've left the classroom. Compared to an associate who had no passion for teaching and always aspired to get out of the classroom so she could get an admin job. And so teaching vs. Admin often depends on the values of the individual.
Yeah, it's sad but generally the case. There are exceptions, of course, but even in the courses for admin certification prof's will causally joke about you being "ready to leave the classroom". It either that or people who were never in the classroom (i.e., phys ed "teachers", guidance counselors, etc.).
Principals are basically low level politicians. They pretend to care about whatever in-vogue changes there are and pretend to implement them in their schools, teachers pretend to do them...and even those that generally try to do them just get steam rolled two years later when new politicians try to make their marks and say "oh, that SBAC test we had you preparing kids for for the past two years is no longer being administered", or "the new Superintendent wants to completely re-write the curriculum using this form....so re-do everything you've been working on for the past two years".
At the end of the day, teaching is a government agency and is beholden to government. It's its own version of The Wire.