There's measurements (say, increase in customer retention as a % after a new feature is deployed) and then there's heuristics (discussing the feature with customers to gauge sentiment, being careful not to fall prey to bias or lead the customer's answers).

My point is that an obsession with empiricism can make you think that only #1 is valid evidence and thus use it for qualitative analysis where it should not be used.

Only using metrics for feedback is giving yourself tunnel vision.