Another strike against p-values

Though I'm asked to produce the darn things every day, I have grown to detest p-values, mostly for the way that people wanted to engineer and overinterpret them. The fact that they do not follow the likelihood principle serve to provide an additional impetus to want to shove them overboard while no one is looking. Now, John Cook has brought up another reason: p-values are inconsistent (in the sense that they do not provide evidence for a set of hypotheses in the way that you would expect--I suspect if they were statistically inconsistent in the sense that no unbiased test could exist they would have been abandoned a while back).