I'll just preface this by saying that I'm not a pod student yet, so I can't really comment on the time commitments for earning another degree. Also, I have a lot of bias towards public health.
I am in an MHS program at a school of public health right now because I wanted to take more courses in public health after graduating from undergrad. I know that I am going to pod school specifically go get a combined DPM/MPH degree because of how much I've learned in taking public health courses and how valuable an MPH can be in concert with my DPM degree.
I definitely think an MPH is a wonderful thing to have. If you're not into public health then don't worry about it, but if you're interested in health populations, health policy, epidemiology, global/international health, addressing health disparities, biostatistics, or just public health in general then it might be an avenue worth exploring. I can say that it will help you see medicine and its applications in a different light.
Actually, there are veterinarians, dentists, DO/MD's, nurses, NP's, and PT's at my school but no podiatrists. I've been asking around and none of the faculty or deans I've asked know of any past, present, or future podiatrists--other than me--matriculating at my PH school. I think that this is unfortunate and am hoping for some more pod representation in PH some day. I love podiatry and it has so many potential applications in the public health arena! Personally, it will be exciting for me to see how the DPM/MPH will fit together.
That said, I definitely don't think an MPH should be a supplement for padding the resume, and I'm guessing that it won't necessarily gain you more patient referrals/contact. It will definitely help you with public health research or the ability to work in a public health department/agency/school/CBO/NGO/fill in the blank if that's your interest.
I can't comment on the MBA, but I am also curious to hear what the use of a PhD would be other than a slight advantage for positions in academia. Isn't a DPM analagous to an MD/DO in that you can perform research without the PhD because one doctorate is enough? I know of a DPM doing clinical research without a PhD, and there is a DPM teaching at a medical center within my university; neither of them have PhD's.