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.

The average (over 24 hours) temperature yesterday was 25˚C. You could certainly ask how that compares to other August 29ths in different years.

This even has a name ("grand mean"), so I'm surprised that someone thinks it's never useful.

> the subsamples have the same number of data points

It's unlikely to be useful in any other situation. Certainly not for averaging the temperature of a galaxy.

Both the overall mean and mean-of-means have sensible interpretations though.

Suppose you observe a random sample of stars and find their temperatures to be 6000, 6250, 6750, and 7000C. The best possible guess[0] for the temperature of a new star drawn from that population is 6500C. The average temperature of all the starstuff may be different if one star is larger than another, but that's an answer to a slightly different question.

In fact, I would argue that the mean-of-means is often a more appropriate summary statistic than the overall mean of the observations when there are repeated measurements.

[0] Under L2 loss, with no prior, etc etc