Why teach in a gubbmint school?
My guess is that it pays more. The public school has great difficulty ejecting persistently misbehaving students, unlike the private school.
The schoolmarm and schoolmaster of old put up with considerably less crap, but also earned considerably less, too. It’s a matter of choosing between the cake and eating it.
I’d still think there would be SOME relatively well off private schools in the area, just given the big money that exists there. Someone has to teach the Trump kids, proverbially speaking.
And if Ms. E. really had to pursue that (public school) vocation — New York City isn’t the place to do it. Do that in Podunk, Iowa where 90% of the students are fundamentalist Christians and/or conservative Roman Catholics — and act like they actually fear God already.