You're conflating different things. People can already choose between public, private, and homeschool. The "credit" is a public resource allocated for a certain purpose under certain conditions. A union doesn't unilaterally decide anything.

You're entitled to choose a non-public school, to want to divert a public resource to yourself with fewer strings attached, and to want more leverage to disregard teachers' stakes in delivering education. Not everyone would agree with your conclusion that it "should" make things better, or that it's even necessary to make improvements.