That's an interesting point. If Catholic hospitals (and medical practices in general) were offering Ob/Gyn services in a manner consistent with Catholic doctrine, that would be a real difference from other health care providers, and worth the Church's effort, in my opinion. However, I don't think that's the case, generally.
I will not even mention the situation with pharmacists! I know many good, Catholic pharmacists who work in chain stores. They must compromise their conscience constantly in order to hold a job.
I remember vividly a story told by Fr. John Corapi who gave a Retreat somewhere in Florida. After the Retreat, a husband and wife couple, who owned a pharmacy, decided to refuse to fill all prescriptions for birth control pills and to rid their stores of all condoms and such. They almost went out of business until the local Baptist Minister noticed their plight and mentioned it in his Sunday service. In time, the word spread and the couple ended up serving only a Pro Life clientele and had four pharmacies!
In my area, a group of women is trying to get a Pro Life OB/GYN practice to come into the area that only uses NFP and practices the Creighton methods. These folks are as rare as hen's teeth. So far, no luck.
Frank