I don't think you necessarily have to have a driver's license to buy a vehicle.
For example, North Carolina recently required its residents to present a valid driver's license or identification card in order to register a vehicle. The DOT FAQ there says nothing about needing a driver's license to actually buy the car. And you can register it with just a state id card, and those cards don't give you driving privileges.
Most insurance companies require the owner to have a valid driver's license before they will insure the car, so from a practical standpoint, you may need the license.