What's wrong with the average temperature over many stars? It gives you the best possible estimate (in a MSE sense) for the temperature of a new star for which

What's wrong with the average temperature over many stars? It gives you the best possible estimate (in a MSE sense) for the temperature of a new star for which you know nothing about. It may not be a great estimate (e.g, the distribution is multimodal because stars come in various types), but it doesn't seem obviously nonsensical.