I think it's important that we're all exposed to each other, as well. Having specialty schools, particularly if they are ethnic/religious, segregates us from one another.
We're better at diversity, I think, when we experience it in our daily lives.
I agree - there should not be a publicly funded Catholic system, because there aren't any other publicly funded religious education systems here, and because we should all go to school together, in the first place!

There are some ways that schools can influence parent involvement, but they all cost money!