M. Erez Kats, Seattle Language Arts Teacher
I don't know if private schools are killing the public school system, mainly because they seem to operate largely in an independent manner from public schools. They don't really attempt to advertise or take a more prevalent role than public schools in most (if not all) places I've ever lived. People seem to already know about private schools, and if they want their kids to attend those schools, they actively seek out admission on their own.
I believe that as long as you have low-income families and low-income people in any location, you will always have a need for public schools though. These families simply cannot afford to send their children to expensive private schools, as much as they'd like to. And scholarships are in high-demand and short-supply. The parents that choose to bring their kids to private schools are also typically familiar with the school and what it offers. They want a very specific experience for their kids, and a very qualified faculty that they can remain loyal to. I believe that parents know what they are going to get from a private school often times, whereas they feel like they are getting something from the grab bag or drop of a hat when it comes to public school teachers.
Charter schools further complicate things in that they are not exactly private schools, but are very similar to them in terms of the way that they are run, curriculum, and the overall student experience, etc. Parents may feel as though they have a much more privatized and personalized education for their child, and they feel more empowered or "in control" at this point.
But public school is something with so much history and tradition behind it, and so often is something that "just makes sense" to families when they move to a new city or neighborhood. It's a way to integrate a student into a school as well as an entire city. And they have the government $$ backing them for the most part, as well as the incentives and possibility for growth that often makes it such a popular choice, both on a district level, and in individual schools. For this reason, I don't believe there will ever be a complete takeover. Public schools will always have their niche, and I don't believe today's society is quite ready to do away with all of that just yet.