Now that we've all said "feature selection is not dimensionality reduction" to our hearts' content, could we return to the point of the article?
Regardless of whether you're doing feature selection or dimensionality reduction, the point remains that, if you're doing supervised learning, PCA is just compressing your X space, without any regard to your y. It could be that the last principal component of X, containing only 0.1% of the variance, contains 100% of the correlation between X and y.
Using PCA for dimensionality reduction in a supervised learning context means throwing out an unknown amount of signal, which could be up to 100% of the signal.
Now for unsupervised, exploratory analysis, PCA is definitely a candidate, but there are plenty of often-better alternatives there too.
Regardless of whether you're doing feature selection or dimensionality reduction, the point remains that, if you're doing supervised learning, PCA is just compressing your X space, without any regard to your y. It could be that the last principal component of X, containing only 0.1% of the variance, contains 100% of the correlation between X and y.
Using PCA for dimensionality reduction in a supervised learning context means throwing out an unknown amount of signal, which could be up to 100% of the signal.
Now for unsupervised, exploratory analysis, PCA is definitely a candidate, but there are plenty of often-better alternatives there too.