Okay, well, with a cut-down population, you also lose the labor required to produce to support the population. Then labor becomes a short resource. Without a labor reserve, you can't take advantage of technical progress, and so the economy becomes unstable and poverty becomes more wide-spread, rather than the normal model of developing better access to food, clean water, and healthcare as technology improves.
This flies in the face of history. Cut-down populations lead to boom times of reduced poverty and inequality (most notably after the black plague). A terrible way to get a boom time, but that's what happens.