I believe great product leaders actually lean more on intuition than data.
Good data is important but it's open to divergent interpretation, usually leads to more questions, and is better at tracking well-defined goals than it is answering hard questions.
Intuition is founded on a deep understanding of the customer built up by countless months and years collecting anecdotes, spending time with customers, and reflection. A strong point of view can only emerge from living and breathing the problem, not just from surveys and data.
A great product strategy, roadmap, and culture can only come from a strong point of view on the customer's problem.