The main reason why large chain stores (and any other kind of stores) should continue to do this is because it reduces the prices that they can charge their customers. This helps the customers and it helps the stores. This is not, then, a moral or ethical argument. Instead, it is an argument based solely on the economics of the situation.
When large firms engage in offshoring, they generally get their labor for lower prices. This ends up being a benefit to consumers in the United States. These consumers get lower prices and can therefore afford more goods. When large chain stores lower their prices, they can often gain market share. Thus, offshoring their production tends to be good, at least in the short run, for both the firm and its customers.
Of course, there are arguments to be made against offshoring. But, if we are arguing that firms should engage in offshoring, we must argue that offshoring is good because it gives lower prices to consumers and greater market share to the large stores.