Not that many years ago we would use children for all manner of things we deemed necessary - cleaning chimneys, selling posies, picking the pockets of well to do gentlemen. Then, quite rightly, we realised that this was not a responsible way to treat these innocent souls but we needed somewhere to keep them under control whilst we got on with doing grown up things in a grown up world. Schools were basically child prisons and it made sense that whilst they were all in one space we teach them stuff so that when they were old enough they could clean chimneys and sell posies immediately and make up for all that pesky time they had lost being a kid. I'm sad to say there are schools that are like this still.
Of course there are many wonderful schools filled with countless dedicated teachers. Exposure to these amazing people is undoubtedly one of the major advantages of sending our precious cargo to these establishments. I also think schools are very helpful in achieving the elusive goal of raising a 'well rounded' individual. It might be challenging for one family to ensure a child gets the measure of twenty or thirty subjects. That being said being an all rounder is all very 90's, specialism is the new black and can you help grow a handful of extra special talents? Absolutely! Venus Williams totally homeschooled; Taylor Swift homeschooled up to the hilt and they are, obviously, very successful. As your question was about academics perhaps these examples aren't helpful but then my question to you is, how important are academics really?
I'm not saying the ability to read is overrated but I'm a strong believer in that quotation about the dude and the fish. One salmon supper will keep him full for a day but a rod, some waders and a few tips on the best bait and he will eat for life. Our aim as parents should not be to shove academics into our kids brains like education is an all you can eat knowledge buffet but to foster a desire to learn and encourage the confidence to learn independently and if you want to do that at home I have no doubt that you can.