Ask HN: Feedback on a non-profit idea to expand access to private grade school?

So I was tossing this idea around and I wanted to get feedback from any of you - especially those of you who may have kids in private school now.

I was thinking of making a public, tax exempt charity that would take in donations and issue grants to students and schools to help them pay for tuition at private grade school (K-12). Ideally, parents would donate to this organization about 10% more than what the tuition would normally cost, and then their kids would apply for scholarships that the organization would give out. The net effect is as follows: 1. Parents get a tax deduction for donating to what would effectively be a scholarship to their kid, and although they're paying a larger nominal amount, they get a higher net benefit if their tax rate is > 10% 2. Schools would be able to get more funding, and the organization would use these excess funds to help kids who normally couldn't afford private school to get in.

The parents' donations wouldn't be earmarked to their kids, but because they'd be giving more than what the schools need there would be enough for more than the kids who would be applying for scholarships, and therefore we could expand the enrollment to disadvantaged students, or help schools expand their facilities, or hire new teachers.

As an example of my napkin math:

Tuition: $10k Parent's income: $100k Tax rate: 20%

Parent donates $11k to the organization, their kid wins a 10k scholarship. Parent's net income after tax is: $89k * 80% = 71.2k

Parent's net income normally: $100k * 80% = 80k - 10k tuition = 70k

Does anyone have any feedback? I'd appreciate if we kept it non-political.