That sounds like a traffic control problem, a public transportation problem, and an event planning problem related to specific events rather than a need for medallions.

Once the people are already there, they need to get home somehow -- what do you expect? How do fewer taxis help the problem?

"That sounds like a traffic control problem, a public transportation problem.."

All those things come into play when regulating how many registered taxis are allowed on the street. Or the decision to regulate at all. Also its one of the sticking points for locales as to why they want to regulate operators like Uber as local planners need to be aware of them and their numbers.

"..and an event planning problem related to specific events"

The venues don't really have a say in who parks out in public streets, they can raise complaints if it becomes a problem though and often try to cash in by hiring services themselves. The more monied customers will most likely not ride the meat bus over to a public transit hub though.

A licensing system would be more flexible there, as you could have categories of licenses to handle different types of demand -- rush hour taxis, etc. With a medallion system, every holder has a heavy financial incentive for their cab to be in service 24/7, due to its very high cost, meaning that during special events, you can and will get an excess in cabs.