One might assume. Possibly the biggest trouble of dollar stores is that a lot of the "deals" are the result of simply selling things in smaller quantities. The next time you visit a Dollar Tree, compare the actual amount that you get for something like flour, oatmeal, detergent... really anything, to the sizes sold at normal stores. Things are often cheaper at Dollar Tree and Family Dollar because the containers are smaller, often 2/3 size, and sometimes the price for goods at dollar is more than elsewhere when adjusted for quantity. There are some deals to be found at Dollar Stores, but it's not as if similar deals can't be found at normal stores. Dollar Stores compete because of perception.
I occasionally stroll into a 99 Cents Only store and there was a time when they had big juicy mangoes for 1/3 of the price of the mangos at the local Ralphs or Vons. I bought some on the spot and they were delicious. But that's one of the ways that dollar stores get new believers; they will have a few really good deals on things that aren't really essential, like mangos, to get people to think "wow!" and assume that all the other low prices around them are just as good of a deal.