This approach can mislead people because it by design make the hypothesis that the support is infinite and that the variance is finite, which is why it ends in a thin tail distribution in the first place.
Plus as said by klodolph the choice of arbitrarily restricting your knowledge to the mean and to the variance as summary statistics will lead to the Gaussian distribution. Moreover in practice restricting arbitrarily your knowledge is a violation of probability as a model of intuition as showed by Jaynes
Plus as said by klodolph the choice of arbitrarily restricting your knowledge to the mean and to the variance as summary statistics will lead to the Gaussian distribution. Moreover in practice restricting arbitrarily your knowledge is a violation of probability as a model of intuition as showed by Jaynes