Not necessarily. My kids have to public school from kindergarten. My oldest son goes to a high school in a lesser desirable neighborhood because they have an IB program. He scored a 1330 on his first SAT attempt and a 31 on his ACT with no prep class. It’s just that we are involved parents and he is a motivated student.
Good for you....
I was making a generalization, which I would have thought was obvious. Clearly, you and your family are an exception. I’ve also had one go thru public schools successfully, but that again was an exception.