In the old days, there weren't any doctors that had a medical call center. For that matter, there was a time before doctors even had a telephone! Eventually, however, shortly after it's advent, doctors did start using the telephone. Then, they started using the answering machine. (Some still do!) After the answering machine, of course, came the pager, and then the cell phone. As convenient as cell phones are, they are also obstacles to spending more of your free time doing the things you really want to do, being with the people you really want to be with. That's what having a medical answering service is for.
Of course, that's not all it's for. A medical answering service will also help you more fully convey to your patients that you're really there for them. Still, giving you more free time is a big part of its appeal. It benefits both of you. If you're the patient, you may want to strongly consider finding a doctor's office that give you some way to get in touch with them twenty-four hours a day. On the other hand, if you're a doctor, then knowing that patients are looking for that should increase your interests in the services of a medical answering center even more.
Either way, it's certainly better than an answering machine. By using a call center, your callers will get to talk to a real live human being. Everybody prefers that. Also, an answering machine cannot distinguish between someone who simply wants to leave a message and someone who is wondering whether or not they need to go to the emergency room. A human being can, and can therefore page you in the event of any medical inquiry. While it's true that this service is more expensive than just using an answering machine, you can't really put a price on the kind of peace of mind it offers you and your patients.