Shouldn't cities cancel medallion systems if they are allowing Uber and Lyft to operate?

Medallions can be transferred. Often sold and bought privately.

Should the price companies paid for medallions be refunded?

The rules are different in every city, but in many, the medallions of cities like NYC and Boston are being sold and bought as private property.  Taxi medallions, the license to operate a taxi, can be transferred from owner to owner, so taxi companies considered them as being commodity and put values on them.  They are being traded freely from owner to owner.

"Often called medallions, these licenses constitute a form of private property. They are routinely bought and sold, leased, used as collateral for loans, and count as assets in bankruptcy." - (Problematic Private Property - source)

Medallions are supposed to be a way to limit the number of taxis to not saturate the market.  They have all started as flat fee, but now some cities can be seen charging the street value upon issuing them.  

As the deregulation moves forward and it becomes "official", the medallion system will be phased out and soon be eliminated.  As these events take place, some experts believe there shoud be buy backs.  Here's an excerpt from Boston Globe (source):

BUY THEM BACK. Call it the ultimate mea culpa by city transit authorities who made taxis buy medallions and did little to stop Uber and Lyft from flouting them. Adrian Moore, the vice president of policy at the libertarian Reason Foundation, said a medallion buyback could be seen as a sort of middle ground on a spectrum that runs from cracking down on ride-hailing apps and completely deregulating the car-for-hire business. Say the value of a medallion were $150,000 in some hypothetical city, for example, and in scrapping medallions, city authorities might reimburse owners $50,000. “[Medallion owners] made their bets on how the world was going to be based on a set of laws, not on the marketplace,” said Moore. “Maybe we bear part of the blame, too.”

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Uber Driver, CEO of TaxiFareFinder and Unleashed, LLC