I think we can agree that whether home school or traditional school building structure is required. For that matter, so is a formalized curriculum. The difference I think for the homeschooled, the parents can give more time to the areas of interests to the child. Skills requiring further analysis can be applied to topics of interest. Those areas where the child quickly masters and doesn't wish to go deeper, can be dealt with fairly quickly. I only WISH that classroom teachers could do the same! Some kids find ancient history, especially Egypt, Greece, or Rome fascinating. Others want to rush through and get to 'current history.' LOL! Both are fine especially for research purposes, yet in order for practice to be given, the instructor does have to make some of the choices on when and to how much time will be given.
Of course one can vary the students selections, but if a kid really doesn't care about a certain topic, pretty hard to get their best work.
Math is even more of a 'home school' ready subject. If fractions are 'tough,' more time can be devoted for real understanding. Indeed, cooking and trips to the grocery can be repeated and lessons applied. Once that is nailed, decimals will come much easier. Perhaps the kid is just truly talented at math, instead of pre-Algebra in 7th grade, they could already be in Algebra I. The student can move as slow or fast as mastery takes them.
General schools are getting better about using computer math mastery programs, but the very nature of schools frown against huge gaps within classes. There is also the lack of 'hands on projects from real life, that successful homeschools naturally apply. Simple, one cannot take 30 kids to the grocery for a field trip and mock groceries in classrooms, even in 3rd grade tend to get out of control.
Science projects at home can not only be performed by the child, he can design his own experiment. That's individualized and really too much for a regular classroom, even with a great lab set up.
Novels, textbook readings, poetry, all can be done both aloud and to self. Parent and child reading the same books, at the same time and discussing leads to closer relations. Now I admit that I read aloud to my kids from the time they were born-high school. Why? In middle school one was struggling with "Julius Caesar." I said, "That has to be read aloud, you can't understand it by reading silently. So the three kids and myself divided up the parts and read it aloud. Now that child wasn't crazy about Julius Caesar, loved "Romeo & Juliet." Until college, was not assigned any more full length Shakespeare. However, all of my kids enjoyed the comedies, we read those at home. They liked 'drama.'
Even British Literature AP courses are going to keep the kids in the same book or two. Has to do with evaluation and covering certain aspects of the readings. Homeschooling allows more student choices and types of evaluation.