I think both are extremely useful in different use cases. For example, most successful startup ideas come from anecdotes:

"We've been working in x for 10 years, that's why we know this really niche thing is actually a big problem"

I can use usage-based billing as an example. Unless you've worked on a billing system as an internal systems engineer or monetization product manager, you don't know how much of a resource-hungry mess most billing systems are.

You could try to run a survey to gather statistical data, but it'd be extremely hard to actually find enough billing engineers and monetization/pricing PMs to get significant data.

In this case, the gut feeling ("this sucks in every company I've worked at") is better than the data.