History is complex and so determined opponents can always find alternative explanations that they consider plausible. Very rarely are there historical cases that prove to knockdown all opposition. That’s why finding cases in which several plausible factors are similar is helpful. Hans Hoppe refers to this in comparing the economic performance of East Germany v. that of West Germany as demonstrating the superiority of a freer market system.
By extension, the comparison between the downturns of 1920-21 and 1929-1933 have a similar advantage as historical evidence.
One could point to the experience of Western economies in the 19th century, which experienced panics instead of depressions, the latter of which involved serious unemployment. The U.S. economy did not experience severe unemployment in a downturn until the depression of 1894. Bob Higgs, in his book Crisis and Leviathan, argues that the rise of labor union violence against private property contributed to the problem.
The colonial period in America experienced remarkable economic progress largely free from boom and busts and unemployment. Even though Great Britain had a central bank and credit expansion, the British did not allow banking to develop in the American colonies. Murray Rothbard chronicles this in his multi-volume work, Conceived in Liberty.