Government-run schools (and their privatized counterparts) are not going away. Here are two very different reasons why.
First, most people in power today got there by successfully working the school system. They are the top 5% students. Now, this may also explain a lot about the condition of the world today, but that is a different issue.
Second, schools provide free day care. For this reason alone, they will always attract a majority of families.
Having said that, homeschooling isn't going away either. Again, here are two reasons.
First, parents will always have more control of their children than the state.
Second, homeschoolers can march on government offices very effectively, because they love and use technology, the event is a perfect contextual "unit study on government," and homeschooling students testify VERY well. And because government organizations can't even afford the students they currently have, adding more is anathema.
Having said that, children and parents on both sides can easily fall into the habit of treating people who have made different decisions around schooling as wrong, or even corrupting. This could be tragic. More than ever, the two sides need to learn from each other. The future is a spectrum of choices. That groundwork needs to be established today.