Currently hypothesis tests for normality are setup so that the null hypothesis is that the data is normally distributed and the alternative hypothesis is that the data is not. This seems to have problems where either you have a small sample size the test is underpowered and will fail to detect a meaningful deviation from normality, or you have a large sample size and the test rejects normality even when the departure is inconsequential.
Doesn't this problem mainly stem from the way normality tests are set up? To me it seems to be turning the hypothesis test logic on its head. Would it not make more sense if the tests were specified the other way around so that the null hypothesis represents the data deviating meaningfully from normality and the alternative hypothesis that the data is sufficiently normal? Then you would need to achieve enough power to be able to reject the data deviating from normality, so underpowered tests would not let you get away with assuming normality, and very high power wouldn't hurt because the test only rejects if the deviation from normality is big enough to be a problem.