They found that promotional pricing generates more revenue. Moreover, it's hard to switch from promotions to EDLP. One author, Harikesh Nair, explains the findings:
“Now we have empirical evidence to show why most stores chose PROMO pricing and stuck with it during a competitive shock — it earns more revenues and is too expensive to change."
I think the research seems framed in terms of whether EDLP is better or worse than promotional pricing. That's the absolute wrong way to frame the question. EDLP worked for Walmart because it fit well with the other choices and activities in its value chain. Other grocers had very different activity systems. EDLP couldn't just be dropped into those systems. Everything they did fit with promotions. Change to EDLP naturally was costly because it required many other changes to maintain organizational alignment. The lesson is clear: There is no one best pricing strategy. It's all about fit. Competitive advantage comes from an aligned system of activities throughout the value chain.