Avinash,
I think what you recommend would happen if "vouchers" were available... if people could take their tax dollars for education ANYWHERE...
I should also say that Albuquerque has a thriving network of private schools that has developed because Albuquerque Public Schools (APS) are such a mess.
APS has reached critical mass - in that it now lives just to grow and get more money and power. No longer is education Job #1. If it were it would split itself in to more than one district.