Speaking purely in terms of effects on America (not other nations), I don't see why the Great Depression didn't quickly balance itself out. Both consumers and suppliers were poor, and I can't imagine that the same suppliers (merchants, shop owners) that were selling to the extremely poor were selling to the extremely wealthy. So why didn't the classes, being extreme opposite, divide and balance out? Obviously the upper class needed no help but I don't see why poor suppliers and producers balanced out with the poor consumers to make two balanced classes, and therefore a balanced nation. So what prevented this?
Because prices and wages are "sticky".
I think what you are asking is: why didn't the market quickly adjust to a new market-clearing price level? I.e, if a general fall in income reduces purchasing power of the poor and middle classes, then why do prices not fall in accordance with a fall in nominal income? If joe average can't afford a $5 loaf of bread, why not lower the prices down to $1 so he can afford it so that Joe has his bread while the baker gets a least $1 of revenue instead of $0?
The Keynesian explanation is that wages are "sticky" meaning that it's very very difficult to impose pay cuts on someone's nominal wage. In effect, if you try to tell workers that their next month pay is going to go from $300 to $150 tomorrow, there is going to be serious blow-back from it (i.e labor strike, rioting).
But unless you can cut wages, you can't cut off price and stay in business because you aren't cutting costs. So in reality, when prices do fall businesses quickly become unprofitable, thus laying off additional workers and cause an even steeper drop in prices, which in turn forces more businesses to go bankrupt. This is something known as a "deflationary spiral" and a big part of why the great depression went from a financial crisis into a crisis for the real economy.
In theory, on the long run, prices and wages will eventually adjust at lower levels. But as Keynes say "on the long run, we are all dead". This is one of the major reasons why governments and central banks takes a relatively proactive role to run either monetary or fiscal stimulus in response to recessions and aim to prevent deflation at nearly all costs.