Let's say your family has four kids. As a family, that's large. But as a classroom size, it's really small. That gives you an advantage as a homeschooler over a public school teacher.
That might've worked if we funded schools & gave students who fell behind significant interventions & 1x1 attention, but that's not what happened. One of my friends has a very bright and talented fifth grader in a class with multiple students who can barely read or write. Guess who gets the most attention from educators? Which group the teachers structure the class for?
I find it difficult to wrap my head around you can make it work teaching the entire curriculum for 4 different grades encompassing reading/writing, math, history, science, art, music, etc... I guess its potentially compensated for by the fact that they are all getting very individualized attention, but thats spreading a parent very thin.
Especially when we are talking about high school levels, where you can even potentially go into AP courses- no way a single parent can teach college level calculus, History, CS, etc... effectively.
For all the flaws of our public education system, I don't see how this can work better.
When you have a class size over 20, teachers are forced to be a lot more systematic, which can improve the effectiveness of their teaching. Good teachers make heavy use of social proof. When I tried to teach my kid at home, it was a struggle. But when the kid is around his peers in a classroom, and they are going along with the teacher, he naturally falls in line with no cajoling, etc.
If there were only 5 students, the likelihood he'll just go along with things is much lower.