[spekcular]

But here the issue is the uncorrected multiple testing and under-reporting of results, not the p-values themselves. Any criterion for judging the presence of an effect is going to suffer from the same issue, if researchers don't pre-register and report all of their analyses (since otherwise you have censored data, "researcher degrees of freedom," and so on). This is really a a problem with the design and reporting of studies, not the analysis method.