Catholic charter schools?

A few days ago, Paul Moses blogged about the recently announced decision by the Archdiocese of Indianapolis to convert some Catholic schools into (public) charter schools . . . and to run those schools through "a corporation that it controls."

I realize that many well meaning people have a different view, but -- in my opinion -- this is a bad development.  Catholic education is a treasure, and it is (to put it mildly) in crisis.  This move by the Archdiocese of Indianapolis is not an effective response.  There are exciting things happening -- glimmers of hope -- in Catholic education; moves like this are set-backs, I think. 

Now, I do not think that the Constitution, well understood, prevents the Archdiocese prevents it from doing what it is doing.  If it is willing to run no-religion schools, then the Constitution does not forbid them from doing so.  But . . . why would the Archdiocese, given all the givens, what to run no-religion schools?