We already have school choice for universities. You go where you want and you either pay for it or find funding from the government/charities. No one finds it weird that you're not tied to your local neighborhood for higher education.
We already have something that's not too far from school vouchers for universities, which is FAFSA. The government provides aid that you can use at any accredited institution, not just the institution into which you were geographically zoned.
But does it scale?