I believe the rationale is not a "measurement" of popularity but 1) an assessment of activity, i.e. it will take a certain amount of dedication and time to log stations as a listener, combined with 2) an assessment of the listener's abilities when, for example, the requirement is to log and confirm a certain number of DXCC countries or similar achievements. An implicit assumption is probably that the SWL will progress along a learning curve (about equipment, propagation, operating procedures etc).
I am not aware of any country employing such a requirement at present. However, pre-1990, amateur radio beginners in the German Democratic Republic typically started out as listeners. One condition for advancing towards a transmitting license was to log and confirm a number of different countries, participate in SWL contests, or meet the requirements for certain SWL awards. Similar rules may well have been in place in other Eastern European countries at that time.