Just to correct a few hasty stereo types here:

States run and fund the public education system, not the federal government.  The FED gives grants to the states - the states provide the primary funding, set the school standards, and essentially are responsible for the administration.

I AM a believer that private enterprise will nearly ALWAYS do the same job better and far cheaper than any "public" government run apparatus.

Trump's plan is only to right a wrong long practiced by the so-called "public good" - forcing people to pay for an education system that they believe either is not up to par does not match their own family values.  

The "progressives" never complain when Obama and the elitist Democrats send THEIR children to private schools - ONLY when someone wants credit for a .Christian school that does not suit the Socialist agenda.