Most of us have learned at some point in our lived the concept of supply and demand. That is, the more in demand something is, the more you can charge for it.
Currently, 96% of Utah students attend public schools. Let's say that 1% of children enter the voucher program next fall.
That would increase the demand in private schools by 25%.
There is already a waiting list at many private schools. The schools are not going to be able to take on this additional load.
And, it will allow the schools to increase their prices.
It's simple economics.