If your population’s average IQ is north of a hundred, then you can build and sustain prosperous societies.

That's just completely wrong. You can develop a prosperous society even in below average IQ populations. It's going to depend mostly on your cultural institutions practices. Colonial America is actually a good example, considering most of the colonists were not highly intelligent (and as was standard for agrarian societies of the era), most were illiterate. Instead, cultural practices that promoted and incentivized long-term time preference, planning, and communal co-operation were the thing that made them a prosperous society.

Or a counter-example might be something like the Assyrian Empire. It is fairly reasonable to assume that a Bronze Age civilization based entirely out of a cult that celebrated extreme levels of violence and warfare, where nearly the whole of the population would be illiterate except a 'reading/writing' class of merchants, would have been fairly low IQ. Their civilization lasted 4,000 years. Another example might be the Mayans, Aztec, or Egyptians.

Low IQ civilizations can absolutely exist and be prosperous. They just can't be prosperous in Liberal civilizations which require high levels of individual intelligence due to individual responsibility.