Is it lawful for an industry to be monopolized/controlled to a point where it prevents potential competition?

When the government does it, it's called a franchise.

Monopoly is somewhat different from government controlled industry. For instance, government controlled industry are still answerable to the people (ie, if the public doesn't like it, they can vote out the committee reps, etc). There is no such mechanism for a monopoly, which is why its illegal. Also the GCI's are supposed to be transparent and their documentation, policies, procedures are open to the public (ie committee meetings and open houses to answer questions and issues from the public). Not so for monopolies.

Yes, the taxi industry seems monopolistic and unfair, but its a lot more open and fair than a monopoly -- which has no intention of letting you know why you were denied a medallion or how to get one. For instance, let's say NY, the department of taxis would come out with their survey and studies of what the volume of customers is, and the demand, and how much supply is needed to get to such and such a national average price, and then figure out how many taxis are needed, and then issue exactly that number of medallions.

In a monopoly, there is only one company offering taxi service, and they could put one cab on the streets or flood it so that prices are cheap. It is privately held and doesn't answer to anyone.

Oh and yes, because the medallions are issued, people hold onto them or resell them for profit. Pretty whacked but that's a whole another conversation.

Government does it all the time.

Depends on the country.

In most of the world, yeah it is. We've actually almost achieved what you described, and once we're done, me and my Wall Street boys will tear up the foundations of society.