I suppose the reason for state stores is so the government can be certain that alcohol is not sold to minors. Or perhaps so all profits from this evil are turned over to the state. Utah isn't the only state with a state-run monopoly on liquor stores, there are certainly other. Control of the sale of alcohol has led to some of the strangest laws in the country.
My favorite story about state liquor stores is the huge state store run by New Hampshire just over the line from Massachusetts. It has its own dedicated offramp on Interstate 95. Really, I'm not kidding.
Last time I was there NH liquor prices were reasonable, which is the way to sell a lot of booze. NH makes money because the liquor taxes in MA are very high. Residents of greater Boston drive into NH to stock up. Doing so probably isn't legal but everybody does it.