It is an intentional oversimplification.

Although a good proxy for the situation in the real world is gas stations, as long as you ignore that gas stations tend not to make much, if any, profit on gas sales.

No need to ignore it. This is exactly why gas stations tend not to make much profit on gas.

In my area, there's one notorious gas station that's a couple miles away from any other commerce but has a reasonably large amount of traffic passing by. Amazingly, its prices are always about 50% higher than everywhere else.

Competition works when it exists. Yes, you also have to factor in supply. That's why the phrase is "supply and demand."