If "statistical significance" is just sort of an empty phrase used to dismiss or prove something somewhat arbitrarily. Then isn't the same person writing the same study likely to be just as arbitrary declaring what is or isn't significant .... anyway?
It can't stop you from lying, cheating, or stealing. Nobody has ever not been able to commit fraud because of p-values. There is no formula in the world that can notice when you are cheating in what numbers you plug in...
However, if you know what you're doing, and you're honest, it's really important to know whether you are seeing shapes in clouds or actual patterns. That's what statistical significance is about.
the problem is people leaning on it too heavily and especially obsessing over the 0.05 threshold: so that p=0.049 means your result is statistically significant, you get a paper published and a press release and tenure, while p=0.051 means failure and penury.
the article is arguing specifically against this latter practice, of "bucketing" things according to some cutoff which was literally made up arbitrarily by Ronald Fisher.