The education is not free, someone has to pay for it. Regardless, I have personally seen relatively poor families do very well while homeschooling, and I personally attended a private school that did and does accept students whose parents cannot pay for tuition. Homeschooling, generally speaking, is a much cheaper option than any other method; including taxpayer supported education. And with much better results. Furthermore, one can literally homeschool via an online 'distance learning' program associated with a state funded university for zero personal cost, and the results are similar. They are often called 'virtual schools'. So from a certain perspective, the US could literally homeschool every child willing to participate in that manner with a quality and free-to-them education. Whether or not the results would be competitive to Finland under such circumstances, I would not hazard a guess.
"Free" for the person receiving the education. I'm well aware of how education is funded. As for the poor doing well with homeschooling, would you say that that is the norm, or the exception? Single moms with three kids genreally don't have time to homeschool their kids. Should we just consider those kids screwed and move on?
So your school will admit anyone who shows up at their doorstep, for free? Doesn't sound plausable. That's not a system that will help everyone, just a lucky few.
You have no idea how well virtual schools work, you just assume that it would scale up to any number of participants and somehow be better than how Finland does things? And did you also see how they manage not only to educate their kids, but also make sure that everyone got properly fed so that they could benefit from the education as well?
I'm not saying that this is the best way that will ever be when it comes to education, but compared to everything else right now it looks pretty awsome.