I'd counter by saying that the strongest decades of median real wage growth and general GDP growth were during the high inflation 1960s and 1970s.

I'd argue that the fact nobody was starving at the beginning of the great depression means that the economic mess didn't cause the starvation is a bit of a straw man. Of course, at the beginning, people don't immediately find themselves in destitution, they draw down savings. The destitution begins when the economic disruption becomes prolonged.

I can't find any primary sources on the government policy of destroying food, but I'd conjecture the reason it was done (if it happened) was to support nominal food prices and therefore the apparent credit-worthiness of farms in a highly deflationary environment. Of course, the real problem was that there was insufficient aggregate demand to support the nominal food price, i.e. deflation combined with wage-price downward stickiness caused the market to fail to clear.