Yes, an MD would give you firsthand experience with the health care system, but would keep in mind that an MD is a professional practitioner's degree; it is not a policy degree, nor is it a useful launching platform to start a career in politics. Like I said, if you really want to treat patients, go to medical school. Later, after residency, while you're making some money, you can pick up another degree in policy or economics and possibly combine your interests...that is, if you're still interested in doing such things.
However, if you really want to shape policy and impact health care from a political standpoint, why bother with medical school and residency? You seem to want to have your cake and eat it too. That's the ideal...in reality, you often can't do both without giving up something. Ultimately, you're going to do what you want, but based on your description, you could just as easily accomplish your goals with a BSN/RN + JD or other advanced degree; or, PA + advanced degree of some kind (JD, PhD, DrPH, MBA, MPH, etc.).
An MD is only good for practicing medicine. A JD has more uses other than practicing law, but by and large, a JD is mostly useful for practicing law. An MD-JD won't meet your goals based on what you're saying here. In fact, it seems to me like you really don't know what you want. Have you considered going to the career center at your college/university or talking to your advisor?