Of course, success depends on how you define it.
For example, if you invested $1 in Walmart stock five years ago, and $1 in Family Dollar, guess which investment would give you greater return?
The company that doesn't compete on price. They win. By a lot.
Isn't it odd that in the discount retail market, the company that doesn't compete on price gives investors a better return?
Very odd indeed.
Read the article, in goes into more detail addressing what you brought up.
In addition to what everyone else said, Walmart owns a market other companies don't seem to want: Poor people. Both Costco and Target go after a much richer clientele, and KMart, which is otherwise very similar, is dying. Walmart is the go-to one-stop shopping experience for people working one or more minimum wage jobs.
Related to this is the fact Walmart builds stores where other companies don't. As a result, Walmart owns some very rural markets nobody else is touching.
Edited to add: My point: Given the above, for Walmart, 'cheaper' is a necessary element for success. They're chasing a market that straight-up can't afford 'better'.