Correlation may not imply causality here.
Many of the most successful free market economies embody the concept of "was born on third base and thinks he hit a triple."
The United States and Canada had relatively easy access to territorial expansion, which offered them huge amounts of fertile, temperate land and almost any natural resource needed. They also started with a high-immigrant and relatively educated population.
South Korea got to build their economy late enough to be relatively unburdened by legacy costs. They also had a Western world more than willing to ignore a series of presidents-for-life, domestic crackdowns, and incestuous government-industry relationships as long as they kept Kim Il-Sung up in the attic.
Even Singapore had the advantage of being ideally located for trade purposes.
With those benefits, was the free market necessary to unlock their success?
Conversely, if you dropped (say) the American Founders in 1917 Moscow or 1948 Peking, would they do any better?