A wealth of good points to discuss!
My daughter says that the biggest reason of applying to boarding schools was ending her solitary life as a homeschooler with most friends at adult age, and pushing herself to be more extrovert. When she first got in, making friends was the biggest goal as well as the biggest challenge. On one hand, her introvert character made everything difficult. One the other hand, she had uncommon interests for girls at her age and also with low tolerance for illogical arguments or behavior.
It took over a month for her to make just one friend. But eventually now she has a good group with many close friends in it. She decided to sacrifice academics a little bit to spend dinner and some evening times to hang out with friends, as that was the goal. She may not develop world-beating charisma, but she is already having some change in character that will probably make her adult life easier and richer. And this couldn’t have been done at any day school, private of public, regular or magnet.
For my daughter, the point was “boarding” that spending evening and weekend times for social life was what she wanted, instead of going own ways as soon as the school day ends.