It is ingrained in the teaching of applied disciplines, such as medicine, that measurements of bio-medical quantities in the population follow a normal "bell curve." A Google search of the the string "we assumed a normal distribution" returns $\small 23,900$ results! They sound like, "given the small number of extreme data points, we assumed a normal distribution for the temperature anomalies" in a study on climate change; or "we assumed a normal distribution of chick hatching dates" on a possibly less contentious document on penguins; or "we assumed a normal distribution of GDP growth shocks", referring to macroeconomic changers in markets (bringing up to memory this book, ... and other things).
Recently, I found myself questioning the treatment of count data as normally distributed due to their strictly positive nature. Of course, count data are discrete, making their normality all the more artificial. But even leaving this latter point aside, why should continuous empirical measures such as weight, height or concentration of glucose, deemed prototypically "continuous", be considered normal? They can't have negative realized observations any more than counts do!
I understand that when the standard deviation is substantially lower than the mean, indicating few negative values ("95% range check") it may be a practical assumption, and frequency histograms may support it if not too skewed. But the question didn't seem trivial, and a quick search yielded interesting stuff.
In Nature we can find the following statement on a letter by DF Heath: "I wish to point out that for the statistical analysis of certain types of data the assumption that the data are drawn from a normal population is usually wrong, and that the alternative assumption of a log-normal distribution is better. This alternative is widely used by statisticians, economists and physicists, but for some reason is often ignored by scientists of some other disciplines."
Limpert notes that "the log-normal model may serve as an approximation in the sense that many scientists perceive the normal as a valid approximation now", while noting the low power of goodness-of-fit tests of normality, and the difficulty in selecting the right distribution empirically when dealing with small samples.
Therefore the question is, "When is it acceptable to assume a normal distribution of an empirical measurement in the applied sciences without further supportive evidence?" And, Why other alternatives, such as the log-normal, have not, and probably are just not going to take hold?