Here's the historical development. Abortion was illegal until it was nationally legalized by the Supreme Court in Roe v. Wade January 22nd, 1973. It was legal in three states prior to that, New York, California, and Colorado. There were always some doctors who did abortions on the sly, or who did a D&C for their patients (oops, I guess they were pregnant!). But it was risky and in the medical community there was a stigma both about the procedure and who got abortions, but also about breaking the law and risking losing your license or a jail term. There is a wonderful movie called "Dear Dr. Spencer" about a doc in a small town in Pennsylvania who operated an office for abortions openly, under cover, so to speak, but mostly it was really cloak and dagger stuff. Some doctors gave their patients an antibiotic and referred them to an abortionist, who might be a midwife, or an ex Army medic, or a funeral home director. Frequently the Mafia controlled access to abortion services.
When the rest of the country started to provide abortion services, a mix of the same people, with some entrepreneurs, founded clinics based on the same strategy as any other specialty business: VOLUME. At that time there were still many doctors who performed abortions for their own patients, perhaps one or two a week, or even up to 10 a week, but there was that stigma attached to it, and most doctors realize that getting along in the community is very important to survival. But some people hate to go to hospitals because they can so easily lose their confidentiality or run into a hostile nurse or someone else who knows someone they know, for instance. Also, as larger practices started to form, for reasons of on call coverage, economy, and other factors, it was inevitable that one person in the practice would object to abortions. In larger cities it is still possible to find a private doctor who will do an abortion. (Like on ER the other night Dr. Coburn said, "Abby, I will help you whatever you decide.")
There are a lot of good things about the clinic model however, in spite of the isolation from mainstream medicine that many clinic experience. One is that people who work at clinics really get that pregnancy decisions are very complex and are usually good at understanding what their clients need. (Not always true, some clinics seem to adopt the stigma we are trying to change. I don't get why they are still in business...) Unfortunately, this frees people who just do obstetrics or birth control to miss part of the picture. Like every sub specialty, though, you can assemble a staff that really knows what they are doing, medically and emotionally. I remember talking to one doctor who worked in a hospital setting who said that it was nightmarish having to work with different nurses in the hospital who hated what he was doing or who would inadvertently hand him the wrong medicine because they were inexperienced.
I have given you the long answer. The short answer is stigma. Abortion clinics exist because those in the regular practice of medicine cannot withstand the heat or the stigma of providing abortions. In a society so divided about a subject, and with so much heat about the issue, you need people whose job it is to withstand the pressures, the negative attention, and who are not beholden to referral pressures in the medical community. If that same facility can evolve as an understanding place to go with a pregnancy crisis, then that's turning lemons into lemonade.
I find that it's immensely helpful to hear from people who actually serve on the front lines of social services and controversial subjects. It's hard to understand how sticky issues like abortion or poverty can be very complex unless you're confronted with the differing stories and the human emotions attached. My husband has been working in different social services for the past few years, and it's been an eye-opening experience for both of us. Suffice it to say that you owe the next social worker you meet a hug.