The Master of Public Health degree is a free-standing professional degree that allows its constituents to practice in a number of different arenas, including Health Policy & Management, Health Education/Behavior, Biostatistics, Environmental Health/Toxicology, Epidemiology, and so on and so forth. Public health careers within and between any of these disciplines varies widely, which makes public health difficult to define so generally outside of explaining its individual parts. The MPH is not terminal, but it can serve as a terminal degree for many (while some choose to continue on to obtain the PhD or DrPH).
When a clinician chooses to pursue a public health degree, s/he typically does so with some goal in mind (e.g., community health programming, etc.). This means that there are some people that go to medical school with the specific goal of being researchers, whether clinical or bench. Some know that they will practice for a few years, but want to work moreso at the administrative level to improve the way that healthcare is delivered. Some just want to practice without incorporation of anything else. Either way, the public health degree is flexible, not finite. Public health is not just about having an additional degree to satisfy one's ego, it is essentially a way of understanding things.
When you consider the traditional medical model, the practice of medicine is focused on the clinical aspects of science. It involves the treatment of each patient on an individual basis. When you consider things from the public health standpoint, you would expand the individual view to one that is population-based, and treatment would instead be a focus on preventing a person from having a disease in the first place (or at least teaching people how to manage their illness so that they prevent further deterioration due to a disease). Thus, having knowledge of public health expands the viewpoint of the clinician to consider things that s/he may not have considered without knowledge of these principles. Each concentration in public health allows for anyone that desires to make an impact on public health to do so in a way that is most productive for them and the most beneficial for the constituents that they serve.
There are many clinicians that practice public health but do not have formal training in it. Public health and medicine were once "one", but made a split inthe earlier half of last century. Now, there is more of an emphasis on public health in medicine. Honestly, it is difficult to imagine medicine without the practice of public health and the understanding that with each patient, there is an opportunity to impact overall community health.
So, to answer your question, the utility of the public health degree is not in actually having the additional letters behind your name, but moreso in the everyday incorporation of public health into your thought processes and practice. Public health is just an adjunct that may allow (not guarantee) you to be a better physician, but medicine is not a necessity as far as strengthening public health - which stands on its own to effect change.
Hope this answers your question.