People's Republic of China has followed. India, not quite.
Nor is South Korea a model of freedom; it was authoritarian, it was and still is protectionist. But it did integrate to world economy. Compare it to North Korea, which started off as equally poor, and which has real, concrete, deadly famines in recent memory.
Same applies to R.O.C. Taiwan; autocratic, even corrupt, but reached out to world market (and as a consequence forced the mainland China to follow).
Singapore and Hong Kong: very free trade all the time, and way ahead of others in the region.
In all of those cases those countries were given tacit approval by the US to enact protectionist trading policies and yet maintain their access to US markets.
However, the mentioned countries integrated more to world trade then most other countries in their region, and as a result they are now among the most developed.
Compare South Korea and North Korea, compare Taiwan R.O.C. to P.R.China prior to impacts of Deng's policy change, compare China and India.
These economies were 'allowed' to develop into rich industrial economies was because America provided privileged access to the US domestic markets in spite of their protectionist policies.
They allowed that because they saw the value of having these countries developed into 'westernized' bulwarks against the USSR's sphere of influence.
They could all easily have remained poor under different circumstances.
I guess the best argument along those lines you could make is that the US depended on imported slaves.
There are clearly ways to exploit globalization to become prosperous - e.g. the asian tigers. But it's not clear to me that historical examples are as useful. There's no way to know but I suspect the American colonies would not have prospered in the current economic regime.