Well as another commenter suggested for one of the possible reasons there are so many charter applications from the Northeast, is that they're multi general residents with family and friends who live around them, and they don't want to give that up, so they pay for private school.

It's a personal choice where finance isn't the sole factor for decision making, factors such as proximity of your support network, the inconvenience of moving versus the quality of the neighborhood you're currently in, etc.

Otherwise you're right, if one was to make a choice purely based on finance and quality of government services, moving to the suburbs is the better option every single time without question.