In short, the product is the educated child, not the education itself.  I can be the world's greatest teacher with a wealth of knowledge, but if I have no students, then do I really have a product?

It is erroneous thinking to want a system in which School A has to take ALL kids because it receives taxpayer funding, but School B gets to remain selective in who it lets in while now receiving taxpayer funding.  If you truly want schools to compete for the better kids, then you need to allow schools to reject substandard "raw materials".  A school can't truly compete when forced to take on the kids that don't want to learn, and just want to cause problems.