.. I saw it in law school, too many get out of undergrad, don't know what they want to do with their life, so go to post grad school.
Cannot echo this strongly enough. Most people appreciate grad school much more once they've worked for a while. You also realize there is more to your self worth than grades and summer internships. Having served as an officer also makes you much more desirable to graduate programs -- medicine, MBA, law, and many others -- because you've actually done something other than go to school and work for a couple of months in the summer. People are worried they will "be behind" their peers; the extra years of maturity and working with others more than makes up for it in a hurry.
If you go the USUHS route, be prepared for a lifetime as a Navy MD. My USNA roommate spent 31 years as a Navy Doc + med school + USNA. Getting out presents its own challenges. There is a world of difference between life as a military MD and a civilian MD. Things like having to make money for your practice, billing and insurance, malpractice, etc. Many do it but some aren't willing to take that huge leap after 20+ years in military medicine.
The bottom line is that everyone should attend USNA willing to enter more than one community. It's like candidates who say: All I want to do is fly. What if you end up NPQ for something that happens at USNA or something discovered at USNA? What is you aren't assigned pilot by the USN? Ditto for being a SEAL or a cyber warfare specialist. The road is even more precarious for those desiring med school. No matter how smart you (think you) are, there is ZERO guarantee that you'll be able to be a Navy MD after USNA. You might not make the cut for various reasons. The Navy could always discontinue the program as they did in the mid-1970s.
The above is not to say that you can't have dreams and preferences. You can and should. But you're about to be in the military. When we all preach "needs of the Navy/USMC" and "Semper Gumby," we know whereof we speak.
So if you really want to be a doctor, go for it. But be thoughtful about going for it out of USNA.