In addition to descriptive statistics and inferential statistics, statistical literacy should include Bayesian statistics and most of all-evidential statistics. Indeed, the crisis lies on not only the lack of knowledge of alternate approaches, but also the poverty of conventional research skills. The purpose of alternate methodologies is to compensate the limitations of the traditional approach. Even if alternate methods were widely adopted, it is likely that the implementation of alternate methods would be as careless as in the conventional approach. There is no guarantee that the quality of research would be improved by introducing new methods alone.
Many people are aware of the narrowness of statistical analysis and attempt to counter against it.
But it is an up-hill battle. For example, at Michigan State University once two professors reformed the graduate statistics courses by introducing alternate statistics such as confidence intervals and effect size. The norm set by referred journals is one of many reasons why many researchers, faculty and graduate students blindly follow statistical testing. We don't have to know the detail of statistics. Medical students are not chemistry and biology majors.