Can you not keep a reputation history for drivers that have a license?

They're not referring to a drivers license here, which would be eminently sane. They're referring to taxi licenses, which are artificially restricted.

40-1-193. (a) No transportation referral service provider subject to this part shall contract with, utilize, or refer individuals or entities to limousine carriers or taxi services that are not properly licensed by the state or a political subdivision of this state, are not properly insured under state or local law, or which use drivers that are not properly licensed under state and local law to carry passengers for hire.

And it's worth pointing out that taxi licenses are really an artificial barrier to entry to keep existing taxi services safe. Atlanta's apparently costs a median 36,000, and in big cities like Boston or NYC, they can run into the hundreds of thousands.

These licenses aren't tied to a driver, rather they usually lease them from a managing company. Safety's got nothing to do with it.

(ref http://taxirisk.com/taxicab-facts-for-atlanta-georgia/)

Is the license the same thing as a medallion?

If they just want to ask someone to pass a test and/or background check, that seems fine. If they refuse to issue one because there is a limit, that works against consumers.

Not necessarily. NYC introduced medallions because a glut of taxis we're clogging vital infrastructure and nobody could make a profit, thus safety and maintenance were compromised. Capitalism does not produce the optimal outcome for consumers when externalities are not part of the equation.

At least here in New York, Uber cars are licensed as limos, not taxis. Taxi medallions are often artificially restricted, but I've never heard of limo licenses being capped.

You are correct. It is completely unreasonable to ask Uber to license there drivers like all of the other transportation services.

Exactly. And using unlicensed drivers is not Uber's one advantage over established taxi companies.