In the U.S., if you're lucky enough to have decent health care, you will usually see a general physician of your choice regularly. The idea is that your doctor over time understands your medical history, lifestyle, etc. better than a doctor seeing you for the first time. Ideally, you develop trust and follow your doctor's advice, and maybe your doctor notices changes in your health in time to prevent the worst of an illness.

People will also develop regular relationships with specialists if they need them for a chronic condition or something like that.