> the only honest choice when all you know is mean and variance
This is said as if it were a realistic set of assumptions.
You almost always know more than that. Frequently you have at least a few samples from the distribution. Often you don't know the mean and variance with any certainty. The mean is relatively easily estimated with a fair number of samples, but variance is rather tricky to estimate with any precision.
Some processes don't even have a variance (or have infinite variance, depending on how you like to phrase it) but any set of samples from them will definitely have a variance. Are you going to shoehorn the normal distribution onto that process? I hope not.
This is said as if it were a realistic set of assumptions.
You almost always know more than that. Frequently you have at least a few samples from the distribution. Often you don't know the mean and variance with any certainty. The mean is relatively easily estimated with a fair number of samples, but variance is rather tricky to estimate with any precision.
Some processes don't even have a variance (or have infinite variance, depending on how you like to phrase it) but any set of samples from them will definitely have a variance. Are you going to shoehorn the normal distribution onto that process? I hope not.