All parents should have the right to send their children to decent schools, not just those wealthy enough to afford it now.
To prevent fraud and gross incompetence, we would need some degree of regulation, "spot" inspections, and disclosures by schools to parents of key facts and statistics (e.g., student-faculty ratio, teacher credentials, etc.). But the real power -- the power of the purse -- should go to parents, who presumably care more than anyone else in the world about their children's success.
If the LAUSD ever manages to run schools well, great -- parents would be able to send their kids there. But in the meantime, we're effectively punishing the children of the poor, and limiting their future, merely to protect a massive bureucracy from competition.
You say YOU "believe in public education?" That's fine. Send YOUR kids to LAUSD. But let other parents choose differently.