It's not that easy. You cannot hold a student pilot license and a private pilot license at the same time. Therefore you have to surrender your private in order to get a student.
As one already holds a medical, a student pilot license can be issued by any FAA Examiner (not medical!) for free without hassle.
But 2 students now have voted for a checkride, although that means at least 600$ higher costs. They just don't have time for all that bureaucracy with the other method (our FSDO is 3h of driving/ 2 flying away :-(