Barring some _exceptionally_ unusual cases - lets say 4th std dev cases, I feel, sharply, that homeschooling is a bad idea.
On a broad social level, it removes expected bodies of knowledge suitable for having a useful society; on an individual level, it leaves them in a bad place for interacting with peers. I also believe that most parents are not qualified to actually supervise modern education past a certain grade level- being a parent is a remarkably easy thing to start doing, after all.
The social interaction is a profound and subtle problem. There's this thing about dealing with the mass of peers that homeschooling doesn't teach - but the work world and other situations require. This is not going to come with homeschooling.
I also note, in passing, that I am assuming that parents are _trying_ to do exceptional education and are not trying to play particularly ideological games. In other words, something roughly analogous to normal schooling goals. However. This assumption does not hold true in much of homeschooling discourse. Much of homeschooling is an explicit religious approach; some of the homeschooling curricula and groups are actually a religious-political project attempting to build political power with an alternative education system outside. So discussions of homeschooling have to address that elephant in the room.
Also in passing, any homeschooling policy worth its salt should ensure that children are simply not being educationally or personally neglected; those cases do exist, unfortunately.
tl;dr: don't homeschool. take it from a former homeschooled kid. send the kid to a good public school, please.