It can work, if done intelligently. My daughter was educated in a homeschool consortium for most of grade school, and then applied and was accepted into a private high school. A consortium works by having each parent teach the subject they're qualified to teach. I'm pretty good at math and have teaching experience, but that job (math teacher) was already taken, by a retired nuclear engineer who also had teaching experience, so I ended up being IT for the classrooms instead.
Side note, you might be surprised by the number of teacher's children who are homeschooled.
The issue in my case was, the doctors (many doctors over many expensive months of diagnosis) concluded that daughter was severely dyslexic and would never read past a 5th grade level. On the other hand, the school had diagnosed her as ADD and insisted I put her on Ritalin. We could not come to an agreement, and I decided (exercising the parental prerogative that so many people in this thread revile) to believe the doctors rather than the teachers, (I'm funny that way) and pulled her out of school.
As far as vaccines go, I don't have much to contribute except that daughter got all her childhood shots including the (new at the time) chicken pox vaccine (because it didn't exist when I was growing up, and i got chicken pox in my 20's, and it was really messy) and she got chicken pox anyway.
I did turn down the gardasil vaccine, after much research. Which I won't bore you with here. Either you're familiar with the controversy, or you can read up on it yourself. Feel free to call me an anti-vaxxer.
Others have pointed out that vaccines are madated by law in Europe much more strictly than (most places) in the US. That's true. It's also true that Europe was much quicker at banning Thimerosal (a preservative containing mercury) in vaccines, an area where the US is still behind.