Special needs students comprise a much wider range than what you think if you believe private schools couldn’t accommodate all or even most if they needed to.Easy answer - They are not equipped to handle them. Secondly the private schools as we know them are there to give students a better education. Face the facts you can't educate a turnip. Many of these special ed students are in the classroom so the parents can have a break. What are going to teach a child who just screams and drools all class yes, it's sad but it is very accurate.
Also, no, private schools are there to cater to more select groups of students than public schools; which is fine.
Special needs aside, private schools can choose not to admit any student they don’t want to. If they’re going to accept vouchers, they shouldn’t have that option…they should have to accept every student that they have the capacity to handle.