No, the Constitution says that the schools must be free,  Molly Hooch says that schools must be local.  Taking kids out of their communities to go to a boarding school in Sitka does not count as providing them with education.

I don't know how 10 became the magic number, but if you do a quick web search, it does appear that that number is used by several other states as well by the number of headlines that talk about schools with fewer than 10 students closing.  I suspect, like many seemingly arbitrary numbers, somewhere there was a lawsuit about a school with 11 students that prevented a closure, and so the number was set.  

You own the airspace 83 feet above your house.  Why?  Because the relevant court case was about a landing path that passed 83 feet over a chicken coop. 

I'm just saying that I don't think you will find your savings here.