In large sample statistics, the normal distribution is often assumed because of the CLT, i.e., as wikipedia states: "Since real-world quantities are often the balanced sum of many unobserved random events, the central limit theorem also provides a partial explanation for the prevalence of the normal probability distribution".
Why is this true? Beyond the Galton experiment, what justifies this assumption? Is there a proof for this or is it just an epistemological justification?