Thanks everyone for your replies. I do appreciate it. I am from the southwest, and presently doing my residency training in the midwest.
For me, car isn't the issue - as I got a lease on a car after I moved to the midwest, so it has my new state's plates and registration.
The thing is that my current driver's license has my parents' address back home, which is my permanent address since my folks aren't planning to sell their home any time soon. If anyone ever needed an address proof, I have no problem if one of my mails got diverted to their home, as I could trust that it would be safely kept for me. That would be a reliable address to contact me, if someone ever needed. If I got a new driver's license here, it would just have my current apartment address.... and I might not even be living in this apartment next year as I may want to look for a nicer place, so I don't particularly like the thought of having an address-proof (like a license) of someplace that I am not even living.
Furthermore, I am fairly set on returning to my home state after residency/fellowship, so I'd eventually have to get another driver's license again after I returned back home in a few years. Additionally, I consider my home state to be a much more desirable place to live (due to no-snow winters) with many more people moving there vs my current location, so in the theoretical situation of there ever being some kind of cap on migration back to my home state, I don't want to ever have difficulty moving back. I actually got a substantial tuition scholarship in medical school due to being a resident of my home state, which requires me to work in my home state for a few years post-residency/fellowship... so I'm almost positive to be going back there (unless I get into a relationship with someone in this area and end up staying here, which would also require me to pay back my scholarship). So at this point, my new state is just for a few years stay for some good quality medical residency training, until I return home... at least I feel this way after living here for only 2 months.
How does one find out which states have reciprocal agreements? It seems the tax situation is another headache I'd prefer avoiding, but I may have to file something back in my home state if I don't change my residence.