I'm a former teacher. In some places, the schools are a real mess despite receiving anywhere from $5000 to $10,000 per student per year (some places pay more, some less). Many of the weakest schools are in inner cities where the children are most at risk. For this reason, some of the strongest advocates of vouchers are minority parents who don't want their children sacrificed to support a failing school system. If you check their voting record, you'll find these parents are far from extreme right wing Republicans.

One definition of insanity is doing the same thing over and again but somehow expecting different results. Simply throwing more money at failing schools isn't likely to generate positive results.

As for Cleveland, I've read that the voucher program is good for either public or private schools. However, it seems the (mostly white) suburban public schools aren't very interested in getting a lot of new minority students. That's one of the reasons why so many of the voucher students end up going to private, mostly religious schools. Another probable reason why so many of them ended up where they did is the proximity of private, religious-based schools to where the minority students live.

The vouchers go to the parents, not directly to the private schools. That's an important legal distinction. For over 50 years, college students have been using programs like the GI Bill to attend the school of their choice, even religious based ones like SMU, ORU, Notre Dame, BYU, etc. Some of these students actually use their money to study religion, as when they choose to become a member of the clergy. The Supreme Court has upheld this practice as perfectly legal largely because the money goes to the student, not directly to the school. Constitutionally, there is no valid distinction between universities and K-12 education.

The name of the game is giving all students the best possible education, not necessarily a public school education. One size does not fit all, and throwing ever increasing amounts of money at failing systems only serves to reward failure.