It costs close the same for the school to teach a class of 30 students as a class of 20 students. If the school gets $10,000 per student, it has $300k for a class or $200k. There are economies of scale. It's why public schools are so militant about attendance - they lose money if they lose kids/attendance. Especially in rural areas where a local public school is already barely viable, the vouchers may lead to their closing. The only options for those parents may be religious academies (of a religion they may not belong to) or online schools of questionable quality. That's why the main opposition in Texas was actually from rural Republican districts.
If public schools are "overcrowded" then that's due to a funding deficit or mismanagement. It's not an inherent quality of public schools. I can say that my children's elementary school is not overcrowded. It is excellent, and considerably higher quality than the religiously affiliated preschool they attended.
The tax cut comes in a rebate. If you were already spending $20k/yr for your kids to attend private school, and they pass vouchers, you now effectively receive a $10k tax rebate. It makes plenty of sense to pay property taxes regardless of whether your kids attend school. I also pay taxes for roads I don't drive on, courthouses I don't use, and firefighters I don't call. Education is a public good. Even if I've never needed to call the fire department, I benefit from it existing. Even if you never send kids to public school, you benefit from having a literate population and workforce.