A big part of the problem is that classical hypothesis testing promises much more than it can deliver. "Rejecting the null with 99 per cent confidence", even with good practice, means something like "there's more than random noise here, and we should look into it". If you start with a broadly Bayesian view of the world, you can restate this as "I've adjusted my probabilities to give a bit a more support to the hypothesis I wanted to test".