You can get rid of the market but you can never get rid of competition. Goods not allocated by market prices have to be allocated somehow and so long as goods are scarce there will be competition to obtain them, if not by outbidding competing buyers with money then by outbidding them in time spent waiting in line, doing political favors or some other method.
What happened in Henrico county is the same type of thing that happens when there is a price control. The diagram below explains.
At the controlled price the quantity demanded exceeds the quantity supplied so buyers compete to obtain the good by, for example, arriving early and standing in line (or stomping on their competitors!). Waiting in line is costly so the total price rises above the money price by the time price. The total price for the marginal consumer will tend to rise so that it equals the marginal value of the good – only when the total price is equal to the marginal value (at the controlled quantity) is there no excess demand.
It’s very important to notice that that the shop owner gets your money but does not get your time. Thus, money expenditures are a transfer but time expenditures are a waste. Money expenditures = controlled price times*controlled quantity. Time expenditures = time price*controlled quantity so the shaded area indicates the waste.
It’s also important to notice that the total price is higher than the market price! A price control, therefore, doesn’t even necessarily reduce prices!