For Pearson, Spearman, and Kendall's tau: (i) neither one of them could detect complex (nonlinear/non-monotone) dependence; (ii) they are clearly very powerful

For Pearson, Spearman, and Kendall's tau: (i) neither one of them could detect complex (nonlinear/non-monotone) dependence; (ii) they are clearly very powerful in detecting linear/monotone dependence. All these results have been documented in textbooks and repeatedly talked in classes for over 50 years.