The 200K is not paid to the government but to the previous owner of the plate. So yes the price is dictated by demande/offer but you are true that by restricting the offer the are artificially raising the price of the plate.

When Uber started operating in Quebec the price of a plate in Montreal dropper to around 160K. That was the major point of dispute, since taxi drivers usually get loans to buy these plates knowing that they can re-sell then anytime. Uber changed that.