I wouldn't put much faith in young children being able to direct their own learning effectively. I'm significantly older and I'm still not very good at it.

I'll clarify: I was homeschooled. My parents always had a set schedule and curriculum. Within that defined structure, I mostly taught myself.

A parent is perfectly capable of evaluating and deciding on a wide variety of curriculum even if they may not be knowledgeable enough to write a Chemistry book.

There's a distinction between A parent and all parents.

Disproportionately more parents in low income areas (where kids have worse prospects already) will have very poor education themselves (possibly struggling with basic reading skills) and also possibly additional problems with drug/alcohol abuse etc. Not the sort of people who will be skilled at choosing curriculum and enforcing study.

You need to meet some homeschooled children. The ones I have seen were, without exception, incredibly curious, eager and organized when it came to learning.

I have met a number, but my experiences are more mixed.

There are some great outcomes, but mostly from children who were homeschooled because they had parents who were quite passionate about education. In many cases the parents were big on constructivist learning theory and able to set up a good environment that cultivates this kind of self-directed learning. My own parents were pretty into that, but rather than home-schooling me, sent me to a Montessori school when I was young, and then regular public schools when older, supplemented with some extracurricular stuff like museums and computers on weekends (in the '80s, Logo tied in very explicitly to constructivist education). That worked out ok, and I feel I benefited from having both the school and the home environments. But I can certainly believe homeschooling would've turned out ok, too.

Another large group (in the U.S.) and with a very different profile are kids who are homeschooled because their parents are very passionate about politics and/or religion. This could be any kind of politics (e.g. homeschooling anarchists), but in practice the largest group are conservative Christians convinced that the public schools are indoctrinating their kids with liberal secularism. That does not turn out as well, and often produces extremely sheltered kids who live in an odd kind of parallel universe where they read only things written specifically for Christian homeschoolers (there is an entire niche industry supporting this). They go to social events, too, but generally social events with other Christian homeschoolers. I've met a few of them, and they have pretty negative views on homeschooling, and many think it shouldn't have been legal. Admittedly I met mostly the ones who broke free of it around college by refusing to attend a Christian college (which would be the expected next step).

So I have pretty mixed opinions; I think homeschooling can work if the parents are quite open-minded, and actively encourage the kids to explore lots of new ideas, not necessarily only ideas the parents themselves like. But I think it can be quite unhealthy for kids not to have an outlet a few hours a day away from their parents, in the case where the parents are more controlling. A public school assigning something provides a nice excuse for students to read things their parents don't like because hey, it's for school.

I'm not sure how it would turn out if it were neither of those two cases, but just parents who felt they had to do it because the local schools sucked too much, rather than out of any special passion for homeschooling.

There is likely confirmation bias in children who's parents have opted for homeschooling because that's what they decide to do.

Forcing ill equipped parents into home-schooling by making the local schooling suck so hard that they have no choice would paint a different picture I think.