>A side benefit is that when someone says "What's the probability that the new purple dragon logo outperforms the old one?", you can give them an answer without backpedaling and explaining null hypotheses, p-values, significance levels, and all that jazz.

This is surprisingly valuable. As a former quant/math person, I am shocked time and again how most self-professed data driven people have no idea about inferential statistics. I've learned over time that most people just want to see data and descriptive statistics, preferably in visual representations, and interpret them somewhat creatively and pretty much non-rigorously.