Take a look at HMOs, such as Kaiser Permanente. HMOs combine the function of insurers and medical providers in a way that aligns incentives (everyone pays about the same, but healthier people need less care and are thus more profitable customers). There are many problems that come with the HMO model (e.g. the potential for low quality care), but when it works, it directly solves the problem you addressed and exists in the US.