Yep, this is the same almost everywhere. You're not going to find many young people who will go to a university to get the qualifications to be a medical professional, and then willingly move back to their middle-of-nowhere small town to do that job, even if it pays more.
The Soviets would attempt to solve it by requiring the graduates to work off about 3 years in the place chosen by the joint commissions from Gosplan/Ministry of Labour/Ministry of Higher Education (those same commissions determined the number of students to enroll in the first place, so...). And this system (called "distribution", as in, "distributing the graduates to the workplaces") was widely unpopular for obvious reasons.