This happened several years ago. The young lady in question has taught in various places since then (none being an urban district though).
My grandmother taught at a private school for half a century...and my father is five years short of hitting that mark himself, also at a private school. I forget pensions even exist....because you are right and they had/have no pension. But lots of people (like myself) have no pension these days. Frankly, debacles like Detroit lead me to believe pensions may not pay out as promised....and I wouldn’t use that as a differentiating factor in deciding public vs private. I do remember my dad worked (and still works) on one year contracts - a little disconcerting, but really not unlike much of the private sector, where you could go at any time.
Confucius say students who don’t want to learn, blame teacher. Well maybe he didn’t say that, maybe it was, ‘you can lead a horse to water but you can’t make him drink.’ Funny how better my teacher got when I read the text.