I can't speak for all medallion programs, but NYC medallions were created to solve a surplus of taxis and associated congestion, low wages, and poor service, at least according to the NYTimes:
As far as I can tell that article implies the main goal of medallion limits was to increase prices by decreasing competition. Which is exactly what I would have expected.
http://www.nytimes.com/1996/05/11/nyregion/medallion-limits-...