Ah, well of course all the Blacks attend Hogwarts, and the Parkinsons too, I expect, but can you imagine how large the place would have to be to accept every magical child? It is the best school by far, of course, but if others want to learn at home or attend those little schools with only one professor, it hardly makes them squibs.
It's strange to see how things change. I don't want to stay on because I hate the idea of being a grown man of seventeen or eighteen who is still subject to all the rules of school and treated like a child. But a young man that age would be considered far too old to start an apprenticeship at home. The advanced examinations - your NEWTs, I suppose, are useful for the career-minded, but of course that isn't something our sort have to worry about.
Yes, only muggles punish children for accidental magic, but all I can say is that to me, that law sounds like cruelty to children. I certainly won't make my own children follow it. As you say, so long as there is an adult wizard within reasonable distance, the Ministry have nothing to complain of. They haven't any business interfering in family life anyway.