Perhaps I'm somewhat cynical, but I believe this is a feature of the human condition, not an attribute of our age in particular. Reason and analysis are tools that are used to justify what we already believe.

Agreed! The so-called "Age of Reason" was the anomaly, and probably not that much more reasonable than our own time.

I think there's absolutely a place for this. I often of the old Henry Ford quote about people wanting faster horses. Data and analytics are great for optimization, but sometimes you need to trust your gut and give people something they didn't ask for to have a breakthrough.