This ends up in a similar contest as the dispute over whether your optometrist or chiropractor "deserves" to be titled: Doctor. Or how about osteopaths or naturopaths over against allopaths? There are passionate people on both sides of the arguments. Issues of training or level of education get intertwined with matters of personal or professional regard and credentialing.
In other words, the debate over who gets to be called "doctor" isn't confined to a single field. Thus, the question comes down to "what kind of doctor, or what kind of degree?" A D.Min. degree is a "professional" degree, and not a strictly academic one. It is a "cut above" the honorary doctorate that different educational institutions are known to hand out as a kind of dignity. The D.Min. should not be regarded as the equivalent of the generally more scholarly rigorous Ph.D. as awarded by institutions other than degree-mills. What actually happens in the real world, well....
So get this: we have this thing in the education industry called an "EdD...."
Andrew and ContraMundum are both right. Doctorates are not comparable between professions, and even in professions, they may mean different things.
For example, my wife has a Psy.D. (doctorate in clinical psychology) which she received after getting two masters degrees, each of which took two to three years of study, and her Psy.D. was an additional five-year program beyond that, three years in the classroom and two of practical training which would be called "internships" in other fields, though "intern" has a formal definition in mental health and applies to only one of those two years. Her doctoral degree, because it focuses more on counseling and clinical work, is considered "lesser" than a Ph.D. in psychology, which is more of a research degree and is the usual degree people choose if they want a career in academia, though some people do serve as professors with a Psy.D. Beyond the Psy.D. and Ph.D. for psychologists, there is also the field of psychiatry. Psychiatrists have a M.D. and are considered to have a "better" doctorate.
As for modesty in degrees, we have seven school districts in our county. Most but not all of the superintendents have doctoral degrees in education; all have at least one masters degree and a "specialist" degree, which Missouri expects for those in educational administration. But one of the superintendents with an Ed.D. refuses to use it, and has told me directly that my wife's degree means something but his degree in education doesn't.
And let's not forget the arguments on both sides about First Lady Jill Biden using her "Dr. Biden" title. I don't object; she earned it. But some conservatives objected to her using "Dr." when her doctoral degree is in education, not a Ph.D.
I think it's patently obvious that the problem of degree inflation is not limited to the D.Min. or limited to church circles.
(ADDITION FOR CLARIFICATION: I didn't say, and definitely didn't mean to imply, that my wife's two masters degrees were an admission requirement for her doctoral degree at Wheaton. They weren't. In the field of mental health, it is not unusual for people to spend five years getting a Psy.D. after their bachelors degree without getting a masters between the two degrees. On the other hand, it is common but not required for people to get a specialized masters degree in a narrower field of counseling before getting a doctorate, which qualifies people to counsel in a broader range of subjects. In my wife's case, her first masters degree was in Christian education from Calvin in Grand Rapids, which is where we met, and her second masters degree was in marriage and family counseling from Southwestern Baptist in Texas. Masters degrees in substance abuse, children's therapy, and other subjects are also commonly obtained by people who later decide to get a doctorate in clinical psychology. I don't know if this has much to do with the D.Min. question, but I do think it points out how the doctoral degree can mean very different things from one professional field to another, and even within a professional field, since in my wife's case there are three different doctoral degrees, Psy.D., Ph.D., and M.D., all of which are legitimate but indicate different levels of training.)