your analogy is apt: in your opinion, a poor person will never be able to afford a Ferrari or a Porsche, so they shouldn't be able to afford top-class education either. Ferrari will never be interested in "competing for the low income section of the market"; they'll happily keep making exclusive and expensive cars, reserved to top dogs, popes and the like.
The "voucher" sort of scheme will inevitably result in the State giving everyone enough money to buy a Nissan Micra, with rich parents "topping-up" to get a Mercedes, Porsche or Ferrari. Which is not much different from what you get now, just a bit worse.
One major problem with vouchers is that they are susceptible to fraud. Current voucher and charter schools are not posting greater successes than public schools. Government services are at risk for innefficiency due to non-incentives, but government-funded private services are at similar risk due to perverse incentives.
For example, higher education IS currently on a loan-integrated voucher system, and it is common knowledge that private colleges are a money pit these days.
The "voucher" sort of scheme will inevitably result in the State giving everyone enough money to buy a Nissan Micra, with rich parents "topping-up" to get a Mercedes, Porsche or Ferrari. Which is not much different from what you get now, just a bit worse.