The OP's argument may be that the normal distribution is often applied to datasets with which it has no innate connection and that can only mislead the applier. This is correct -- there are any number of examples where the statistical reasoning behind the normal distribution is wildly inappropriate to the data set being analyzed. The classic example is a dataset with anomalous outliers, say, a cohort in which one person died in childbirth and another who lived to the age of 120. Average age: 60.

But the physicists who apply this method to their LHC data, and those who apply it to the newer finding of gravitational waves, know exactly what they're doing. The data being analyzed are entirely appropriate to this method, and the conclusions being drawn are sound.