With respect, this is poppycock. If you were trying write a political polemic or to illustrate the concept that “correlation does not mean causation” you have succeeded, otherwise…
Is cheap labor a factor in economic growth? Yes, but so is access to plentiful natural resources, including farmland, adequate transportation and communication, technological innovation, education, etc.
Slavery and indentured servitude was widespread in the early times of the colonial period, but most people think of it as an economic institution established and protected by law in the states of the Old South, brought about by the invention of the cotton gin and the growth of cotton as a highly-profitable cash crop. So we are really talking about half of the states from roughly 1800–1865.
Without presenting an avalanche of statistics one can show that the greater part of American economic and population growth during that period occurred in the North and the expanding West, not the South. The same is true of the Jim Crow-era that followed in the 1870s with the end of Reconstruction and the re-establishment of a pre-war power structure in the South. The West had the railroads, the mines, the crops and the livestock. The North and Midwest had the manufacturing. For the most parts the economic bonanza of the Industrial Revolution by-passed the South*.
The great technological innovations of the 19th Century happened despite the depressed, quasi-feudal portion of the country that was increasingly left behind like a poor cousin. Agricultural servitude produces a low-cost, low risk, low yield return on investment, the antithesis of what innovation requires and rewards. It also provides a tempting liquidity: you can add or subtract labor as needed. But the long-term rewards are non-existent.
Let’s go back to cheap labor for a moment. It’s good to have during periods of economic growth and it contributes to the same, which is why the growing parts of country in the 19th Century served as the receiving end of what might well be the largest voluntary migration of people in history. Sure, immigrants were exploited and discriminated against at first, but, unlike the serfs/sharecroppers of the South they were incentivized to work hard, improve their lives and gain access to societal benefits.
As for the economic changes that started to occur in the US in the 1960s/1970s there is absolutely no reason to think that the end of segregation had any significance. What did matter was the increasing importing of energy sources and the exporting of manufacturing. In addition, infrastructure as a percentage of national spending began to decline** and technology pushed society into a need for more highly educated workers than the system provides.
Does the US have economic problems? Absolutely. Are they related to the decline of racial exploitation. As a political straw man, perhaps. As reality? Doubtful.
*The South began to fall behind in 1815 and never caught up.
**The completion of the Interstate Highway system