I don't think it's a state thing. I'm in the suburbs of Philadelphia, and we have lots of private schools, including a bunch of Catholic schools. There's a big Catholic high school not far from me
Part of it might be the large Italian community that was originally rooted in Philly, but has moved to the suburbs. I don't know of any Yeshivas around here, but the Philly area never had a huge Jewish community like New York does
The state laws require a lot of specialized teachers in private schools once you get above elementary. Not a problem when you have a couple hundred students, but if you're starting a new school, expecting an initial enrollment of 50, it's tough to have the specialists for every subject. Our local Catholic school just started going through High School a couple years ago, after they had grown so much that they had to double the size of their elementary school. The School Board here is strongly opposed to competition. They've had a couple lawsuits filed against them for denying Charter School charters. A couple were for schools that were already certified PA Charter Schools in other parts of PA, but somehow didn't meet the criteria here. They are more concerned about the 'financial losses' from allowing charter schools than anything else.