My youngest dsu daughter placed her three school age children 13, 12, and 9 in online home school. It did not work well for two a girl 12 and boy 9. Neither had the the displine or motovation. The older excelled and is going to a school for the performing arts this year.
My nice and nephews, three, completed this type of education and two now attend Texas A&M.
It all depends on the parental influence and the child’s dedication.
That "school for the performing arts" just screams leftist indoctrination to me. My bias perhaps.
It also depends on the type of learner the kid is, and the style of teaching in the courses. A kid who is a visual learner, with poor listening skills will do very poorly in an on- line course that includes taped lectures. They just won’t be able to pay attention.
Those kids might do better with a type of course that is just reading and comprehending , answering questions following each day’s assignment.
You have to know the learning style of the student and make sure the course is a good fit.