Would you say such a silly thing about Catholic hospitals in non-Catholic areas? Charity is Charity.
The trouble with Catholic systems like the schools and hospitals is that they weren't designed for paid staff. Dedicated and willingly poor nuns and monks handled the work. Now the few nuns left, rather than recruiting more teaching and nursing nuns, generally complain that the Catholic teachers aren't unionized and well-paid.
"Converting the sinner" and "instructing the ignorant," however, are Spiritual Works of Mercy -- in a Christian context. "Instructing the ignorant" doesn't mean teaching them to read and to master subjects like mathematics and geography, it means educating them with the explicit intent of passing along the timeless truths of Christian doctrine.
So there is absolutely no need to spend a moment of my time or a dollar of my money on any non-Catholic who wants to take advantage of the opportunities offered by Catholic schools in education regarding secular subjects -- while openly rejecting any religious aspect of a Catholic education.