This is the crux of the issue - CEOs do need a simple metric to summarize performance in each of their business units in order to evaluate performance and prioritize company resources. Metrics are only useful for decisions if they are easy to understand, and consistently measured. Just as Earnings is used to measure profitability, and Revenue is used to measure growth, NPS is the best they've come up with so far for customer experience. Of course none of these 3 metrics is perfect, but they still need to be measured and complimented by more detailed reporting. To better understand Earnings you look at changes in the component parts, revenue and cost. To better understand NPS you look at the mix of scores (1s, 2s, 3s, etc) and follow up questions like actual referrals, which differ by business (unlike NPS which can be applied more broadly).
The author devotes most of the article pointing out that there are areas where follow up questions would give a richer understanding of customer experience, which of course all NPS proponents would agree with.
What he could do a better job of is trying to convince us why executives shouldn't even attempt to summarize their company's performance in customer experience, just like they summarize lots of other complex activities to report to shareholders. Too many companies focus only on hard metrics like revenue and profits, which is why they find NPS a helpful way to steer the company's focus back to the customer.