If an institution offers a medical service, the service should have an average outcome better than taking a placebo.

That is why governments clamp down on quarks and other fake cures. Even if the service is free. I am not a saint (or even an ethical person) if I offer a cure for fake cancer with free gifts. Even if I believe that I am doing the "right" thing.

If you want to argue that government in India did nothing and so Mother Theresa is justified in operating a poorly run service, you are doing a disservice to all other missionary hospitals doing a better job.

May I suggest reading about Govindappa Venkataswamy? The Indian government was also not keen to give the doctor a hand.

https://en.wikipedia.org/wiki/Govindappa_Venkataswamy