It isn't clear whether you have written or are commenting on a 2,000-2,500 word essay already (if so, please post the link) or whether you are just seeking commentary for a school assignment (so please be clear).
If you are honestly looking at this issue, you are touching on an important question in disciplinary boundaries and questions and how disciplines are supposed to work to protect human survival, health and well-being but currently fail to do, and I'm happy to kick this off with a pithy comment, as an applied anthropologist and scholar who has worked globally for 30+ years and who has also published works on how to evaluate and improve and protect disciplines and sub-disciplines (you can find some of my recent indicators for distinguishing academic fads and for structuring disciplines -- look at my piece on "Law and Development" with my indicator, and "Returning Discipline to the Discipline" in Anthropology, on ResearchGate as well as my works on education and applications and methods, particularly in experiential education/ field social science).
Medical Anthropology today is really a euphemism for "Cross Cultural Public Health" and is one of the opportunistic bridges that Anthropology has created to try to create relevance by grabbing on to existing applied and interdisciplinary fields like Public Health and adding something that is "cross cultural" but that doesn't answer the applied health questions that are key to anthropology like cultural sustainability, cultural restoration, cultural protections (understanding and eliminating war and genocide, that are key public health issues with huge implications).
So, do we need, "Cross Cultural Public Health"? YES, in the applied field/ sub-discipline of public health. What exists in this area today in Anthropology isn't the real discipline of Anthropology. It is Public Health and it belongs there. Anthropology needs to be doing what the discipline was designed for; to protect cultures, peace and rights in ways that have a much greater impact on health but that Anthropologists today are politically afraid to do or do not even think about given how the discipline is being gutted (no longer a social science with social science applications but an humanities that just brings a few cross cultural skills into remaining established applied sciences and social sciences).
I agree with David Lempert regarding why have you posed this query. Nonetheless, it is important to delve into this timely query. The choice of this phrase over other conventional ones itself connotes its distinct significance that you may want to focus on health rather than other allied notions. Nevertheless, it is imperative that the term "medical" in medical anthropology also covers wider meaning beyond what one can assume considering the terminology itself that had often been used interchangeably with biomedicine.
One direction, one can put forth to make it distinct even from medical anthropology, health anthropology can focus only on the various aspects of health, including the fourth dimension adding spiritual health to the conventional three dimensions as per WHO.
I believe that much of what the anthropology of health should propose in this century must inevitably lead us a little closer to the rapprochement between elements that enable comprehensiveness and relevance towards prevention, positioning ourselves as possible consumers of that prevention. Chronic and degenerative diseases are increasing greatly, and the ways to stop them are not the same.