> "populations will grow far above reasonable levels"

This theory was considered state of the art in 1798 (when Malthus proposed it) and refuted by 1838 (when Verhulst came up with a better model, which fits actual population data much better).

Populations do occasionally grow "far above reasonable levels" and then crash, but this requires pretty extreme circumstances. The best example I can think of is the Kaibab Deer population -- various human decisions (killing off predators, changes to hunting policies, changes to livestock grazing policies) caused the deer population to explode over the course of 20 years, and the deer population crashed a few years later as it overshot what the environment could sustain and caused substantial damage. That population curve is more or less A-shaped, with a steep climb and steep dropoff.

Populations in general don't behave that way. Most populations of most organisms we know of have an S-shaped curve, with a steep growth phase and then a leveling out phase that involves very little "overshoot" and very little "catastrophic resolution". (Human population looks to be following exactly such a trajectory, and is on course to level off somewhere in the 9-12 billion range.)