[manarth]

  if the purpose of a license is to verify that a particular person
  or business entity has satisfied some regulatory requirements

That's not always the purpose of a license. In some instances, the license is to regulate access to a particular activity or device (e.g. gun licenses, or driving licenses).

In some instances it's simply a tax on an activity (UK TV license, UK road fund license).

In some instances, it's to manage a resource (fishing quotas).

  then license is basically just an access fee to gain entry to
  a market artificially closed off by the government.

That's not necessarily a wrong thing. In the case of fishing quotas, it's to ensure that use of the resource is sustainable.

I wouldn't argue that it's correct to apply that thinking to the medallion system - after all, I'm not sure the NYC population is going to be 'fished out' by an oversupply of taxis - and if it's to ensure a floor on taxi income so that the taxis meet a certain quality, then there are better ways (e.g. regulation) to do that.

I don't see that the sale of medallion licenses is an issue per-se, but that critiques of license-sales are essentially critiques of the medallion system itself.