Nonetheless, if the purpose of a license is to verify that a particular person or business entity has satisfied some regulatory requirements that allows them to engage in the licensed activity, the ability to sell that license to other unverified persons or entities would seem to defeat the purpose of having a license in the first place.

If there's no regulatory requirements, then license is basically just an access fee to gain entry to a market artificially closed off by the government. It's just cronyism. What is the benefit to the public if the license is not providing some assurance of suitability of the license-holder?

  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.