A typical classroom contains 30 students. The problem is that only half the employees of the school system are classroom teachers. The others are everything from custodial staff to education specialists. If forced to compete for students, it is likely that schools would find ways of focusing resources in the classrooms. In a real way, we already have choice in education, only its means tested.
Affluent parents can afford to send their children to schools of their choice.
Middle class parents have some choice, but to opt out of publically financed education requires financial hardships. The poor have no choice but to accept education from the government run monopoly. Educational vouchers empower poor parents and have the greatest impact potential for impoverished communities. The most common argument against vouchers is that if you permitted parents to select their own schools, it would destroy the public education system. Such an argument reveals the low regard many have for government-run public education.