For the near future, most children will be educated in public schools. Public schools have disadvantages compared with private schools; for one thing, unlike private schools they cannot reject applicants.
Thus, however strong the arguments for school vouchers may be, the majority of American children will be adversely affected if voucher programs “scoop off the cream” and reduce funding for public schools.
I think many progressives support such programs when they’re part of a plan to cooperatively improve education overall. Instead, some of the programs are motivated just by a philosophy of “I want mine. Screw you.” and a pretense that public schools will benefit from their own creative destruction.