As a home-schooled student, I had far more opportunity than most to pursue my own interests. I was able to learn the core subjects at my own pace, instead of being tied to some artificial clock and calendar schedule. I could rip through things I found easy, and take my time if a subject was challenging. It may not be fore everyone, but it was ideal for me.
It also fostered a certain self-sufficiency I saw a lot of my fellow college students lacked later on. I knew how to use reference books and library resources. I knew how to plan my time for study. Most seemed to expect someone else to do that for them.
This is one of my issues with it, because while it might even be great for the child, most parents seem to overestimate their ability to actually teach. Many have no skills whatsoever. This could do more damage than good to the education of the child.
That is a common assumption, but even back then, communities of homeschoolers formed around mutual support, and parents proactively sought out standardized testing to prove they weren't lacking. I consistently scored in the 99th percentile. Nowadays, we also have online tools for evaluation and education. Kahn Academy is popular and free.