Edit, OP I didn't see you wanted to be mainly a hospital administrator.
This might be a controversial opinion so feel free to call it out. Also, my intent is not to be condescending because you're clearly intelligent to have gotten into a medical school so I'm sure you're more than capable to understand your decisions. However, being nearly complete with my first year of medical school, I have no idea why anyone who doesn't picture themselves in clinical practice (managing patients directly) for a large chunk of their lives would get an MD/DO (with one exception being MSTP or funded MD/PhD). You pretty much absorb yourself in the field of medical science and clinical protocols for 4 years of school. This leaves very little time for developing the skills you probably need for an career in administration. Why don't you just get a masters in medical science/MPH alongside your MBA if you really want to learn medical science? When I was in undergrad, there were masters students taking some pretty in depth physiology courses while also learning about epidemiology/business/etc.
On top of that, the cost of a medical education is overwhelming. Medical school is not like law school where you can simply get a law degree and have a vast variety of career opportunities administrator/attorney/politician/school principal to school principal that you're now more qualified for than others because you've spent years studying law. Medical school intensively trains you to be a physician and only that and it's simply too much time, effort, and money to consider unless you plan to be seeing patients.
Now if you're considering becoming a physician scientist, that's a different story because you're clearly still practicing and are getting $ for medical school.
Edit: also, just to clarify, I'm not saying that you shouldn't pursue a MBA with your MD degree and then aim for a career in hospital administration. I do see the practicality in doing both. I'm just saying that you shouldn't pursue an MD degree if you don't plan on spending a significant amount of time seeing patients.