It's not fair to compare how "important" different metrics are to the whole business. A business is composed of and built on top of many sectors. That's why we have Finance team, Sales team, Marketing team, Product and Development team..., and not just one "we're a company" team! Free cash flow is important for business operations. Churn is important to predict sales. NPS, though not directly affecting the "money", might be a good indicator for the marketing team. There are a lot more important marketing metrics than NPS, but for a big corporation's branding team, especially in consumer goods industry, it might be useful to look at the "trend" of their NPS over a long period of time.
NPS has noise just because of its nature of being collected with surveys. Like any questionnaires or surveys, if you design it well, you can reduce the noise.