“Practical relevance” (funny use of quotes here) is the end-goal of statistics, and what makes it worth studying in the first place. On its own, the practice and theory of statistics is actually fairly vulnerable, not exactly “hard” in the sense we’d use for conventional mathematics.

The principles we use for relevance, and other techniques we’ve built upon them are axiomatic: there’s no real reason they persist except as a form of historical convention and necessary standardization.

What makes statistics useful is when it’s able to capture quantitatively something that exists practically, i.e. material phenomena. When the stats don’t square with reality, it’s not exactly reality’s fault, so to speak. It’s the statistician’s job to understand and explain why the statistics, or the techniques thereof, failed. This is the red meat of “hard” statistics, how the field refines itself, and it’s also the most fun and challenging thing about it.

When eye-to-eye with a provoked bear in real life, I’d be curious to see if any statisticians would dismiss it on statistical grounds. My bet is zero because they know the limits of their discipline.

It captures the reality very well. Emotions don't increase the likelihood of meeting a bear.