This is an excellent point. In my work, the interpretation error I see the most among people around be is to confuse significance with the magnitude of the pred

This is an excellent point. In my work, the interpretation error I see the most among people around be is to confuse significance with the magnitude of the predicted effect. I.e. if you use OLS to create a model, it is possible to have a statistically significant beta, with essentially no magnitude. If you look at research on carcinogens, it is frequent to see something like "it is statistically significant that eating chemical X increases your risk of cancer" but when you read on, the magnitude of the effect is "increases risk by .0023%, for a cancer that already has a .6% incidence in the population". My point is that people who are not statisticians (or people who use statistics), tend to be concerned with the magnitude of an effect, and frequently misconstrue the statistical significance for that magnitude.