I really enjoyed reading this piece! Several important points.
It's pretty fun to find this article today, after just writing a piece about one of the problems I often come across regarding p-values: That people blindly use p = 0.05 as a cutoff for significance, and in turn often interpreting variables on either side as "proved significant/insignificant".
In general, I think one of the problems regarding p-values is the widespread misunderstanding and misuse of them, probably resulting from inadequate statistical training for many people using statistics - especially outside academia.
Blindly letting an algorithm find a model with low p-values isn't sufficient when conducting analysis.
I love this quote from the American Statistican Associations statement on p-values:
"Researchers should recognize that a p-value without context or other evidence provides limited information. For example, a p-value near 0.05 taken by itself offers only weak evidence against the null hypothesis. Likewise, a relatively large p-value does not imply evidence in favor of the null hypothesis; many other hypotheses may be equally or more consistent with the observed data. For these reasons, data analysis should not end with the calculation of a p-value when other approaches are appropriate and feasible."
I don't really get the controversy around the p-values. My view is they are an important tool amongst many in the staticians toolbox.
We have more than our p-value-hammer and not everything is a nail, but that doesn't mean a little wacking with the hammer is never warranted.
Yet again, I still have lots to learn about statistics, and despite having an above average amount of schooling in it, I often find my knowledge inadequate aswell.
Your piece was helpful, I hope you will do more of this!