Say a small Christian school charges $N per student per year and is only at 50% capacity.
If a per-student per-year refundable tax credit is established for parents who send their daughters and sons to private schools in the amount of $N and the school raises tuition to $2N, they won’t get new students, and many of the students they already had to that point would leave in protest of the raise in tuition, resulting in a net loss for the school.
However, if the school leaves tuition at $N, the students they have had to that point will stay, and new ones whose parents couldn’t previously afford it will sign up, resulting in the school being at 100% capacity and being more prosperous.
Most Christian schools will follow the second model, as will many other private schools who need to go from less-than-full capacity to full capacity.
Only the most elite private schools that already have extremely high rates will jack them up, and in view of the massively increased competition, even they would be smart not to.
How many good private schools aren’t at capacity?
None in my part of the country.