The problem is that it green-lights private and parachiol schools to raise tuition by an amount equivalent to the tax-break. Like tariffs on imported goods. Let’s say we place a tariff of $2,000 on every imported car. Domestic manufacturers can charge an additional $1999 and still beat the foreign competition.
Not necessarily as the decision rests with the parents and there is competition among the private schools for students.
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.
You are likely correct, especially if you look at the behavior of private colleges whenever there is an increase in federal student aid.