Interesting article by Regina Nuzzo, posted in Nature.com. Indeed, it's not just p-values that are being questioned, but even the Fisher-Neyman-Pearson (FNP) paradigm and the concept of maximum likelihood estimates (MLE).
Here's an extract published on the American Statistical Association's website :
Over the same period, but especially since the 1990s, there has been an increasing disconnect between the traditional Fisher-Neyman-Pearson (FNP) math statistics course and the demands for complex analysis in many application areas. The failure of classical maximum likelihood methods to deal effectively with complex models and the success of MCMC-based methods has led to a similar situation: The undergraduate FNP course does not prepare students for these models, and Bayesian MCMC retraining courses are needed to prepare graduates for these applications.
Other articles discrediting statistical science - the way it is performed today - include:
P-values, confidence intervals, and tests of hypotheses can easily be replaced by this concept, which offers the following advantages: robust, model-free, straightforward to understand even by the layman, and easy to implement even in SQL.