I favor the continued use of statistical significance (e.g., p-values with thresholds) as a necessary (though not sufficient) gateway to the publication of empirical-research papers in scientific journals. This gateway was invented by Karl Pearson, Ronald Fisher, Jerzy Neyman, and Egon Pearson between 1900 and 1935. These statisticians focused on the needs of scientific researchers, though the modern focus of the gateway is on the needs of society.
The threshold-p-value gateway to publication is sensible because it helps journal editors and researchers maximize the overall scientific and social benefit of scientific research. The gateway does this by producing a roughly optimal trade-off between the rates of costly false-positive and costly false-negative errors that a journal makes in accepting or rejecting papers for consideration for publication.
I have recently published a book that explains the logic behind the preceding ideas. The book's title is
The War on Statistical Significance:
The American Statistician vs. the New England Journal of Medicine
The book is aimed at scientific researchers, journal editors, science teachers, and science students. It will also be of interest to some statisticians for its carefully reasoned arguments about the fundamental practical role of the field of statistics in scientific research.
More information is available at war-stat-sig.com.
Donald B. Macnaughton