Nebulous relationship between taxes and growth

This post from Matt Yglesias uses carbon taxes as a prelude to discussing the impact of tax regimes on income growth.  The chart he provides (source unclear), reproduced below, shows that only one event, the Great Depression, has significantly moved income from its long-term growth rate.

Small (and one large) fluctuations around a long-term average

The Great Depression was not caused by taxes.  Just as importantly, it appears that the Great Depression did not affect the long-term growth of income in the United States; drawing a straight line from 1929 to around 1949 on the graph would remove the effects of the crash and rebound, but it would no alter the long-term course of income growth.

The larger point is that we have a poor understanding of the causes of growth.  Of course, there are basics – security, steady food supply, electricity, &c – but we do not know conclusively how, if at all, higher-level factors matter.  Does a Napoleonic or Angl0-Saxon legal system lead to higher growth?  What about a bicameral or unicameral legislature?  Will repealing the estate tax stimulate growth?  Or, to the point of this blog, do higher energy, income, wealth, consumption, or payroll taxes decrease national income?  If not, arguments against such policies have no empirical basis if they warn of economic disaster.