Many physicians and nurses are happy about the Federal Trade Commission’s new rule banning the use of noncompete agreements in employment contracts. But they are disappointed that it may not protect those who work for nonprofit hospitals and health care facilities, which provide most of the nation’s care and employ the largest number of medical professionals. In April, in a 3-2 vote, the FTC approved a final rule prohibiting contracts that prevent an employee from taking a job with a competitor. Calling the noncompete agreements “a widespread and often exploitative practice,” an agency announc…