While it is true that not all distributions are normal, many distributions are approximately normal (or at least, normal in some sensible space that maps onto t

While it is true that not all distributions are normal, many distributions are approximately normal (or at least, normal in some sensible space that maps onto the actual collected data). IMO the amount of ink spilled on the idea that science is fundamentally flawed because distributions aren't always normal is probably too high (especially among non-statisticians), and frankly that's not where statistical analyses usually go wrong. A much larger problem (that has nothing to do with the ultimate shape of the distribution) is stuff like postselecting from a set of plausible models until you find one that finds significant results, and claiming that was what you intended to measure all along (this is why it's important to consider stuff like hyperpriors, much moreso than lack of normality).