It's not an unusual claim: Freedom breeds innovation - people are not only free to think for themselves, to ignore the orthodoxy and established power, but they are raised and encouraged to do it and admired for it (to a degree).

I think it's accurate to say that all the wealthiest (per capita) economies in history - i.e., the wealthiest economies over the last ten years - are in free societies.

Your last point might be true, but it doesn't necessarily imply causality of freedom -> wealth.

It's pretty strong evidence!