Sparta at its peak was 10-20 times smaller than Athens. With such a huge population difference you'd expect Sparta to not even put up a fight, but they did and often won and took over large parts of Greece. So to me it is strange to say that the spartan people didn't punch above its weight militarily. If they didn't nobody would have written about them since they were just another small town in Greece.

The problem with Sparta was their inability to incorporate other people into their culture. An example of a warrior tribe very similar to Sparta but did properly incorporate new cultures is Rome, and they conquered the entire Mediterranean that way. We would probably have called it "The great Spartan Empire" if Sparta was a bit different.

Edit: I think the "myth" part was that Spartan warriors were any better than others elite soldiers. They weren't. But they fielded a disproportionally large amount of elite warriors for their size. Rome did the same, and made their new territories also adopt that culture, which allowed them to just expand and expand.