Yes, the problem is that with null hypothesis testing, the two contradictory hypothesis are usually: "effect is exactly 0.00000000..." and "there is an effect d

Yes, the problem is that with null hypothesis testing, the two contradictory hypothesis are usually: "effect is exactly 0.00000000..." and "there is an effect different than 0.000000000...". The problem stems from the fact that people pit an infinitesimally small hypothesis against an infinitely large one. Rejecting an infinitesimally small hypothesis is very very easy. The tiniest of experimental bias will allow rejection if you have enough data. It would be impressive if "There is an effect different than zero" was rejected (but no one would ever be able to do this). Science should try to reject finitely large hypotheses, at a minimum something like: "effect is larger than some reasonable margin to account for experimental bias and imperfect tools". At least a small chunk of the hypothesis space should be rejected for your experiment to be worth something. You sorta get that with confidence intervals since you can see how far the lower bound is from zero.