No schools will accept the vouchers: Elite private schools are very selective and a voucher would not cover tuition. Many private schools would refuse vouchers if state accountability tests or standards were required.
Every voucher program in the U.S. has plenty of schools accepting vouchers. The Edgewood ISD private voucher program found students attending 57 different schools in the first year of the program. (An Evaluation of the Horizon Scholarship Program) The average tuition, nationally, at a private school is $3,116. (Private Scholarship Programs: A Matter Of Priorities) Clearly there are plenty of non-elite schools.