I agree with your point and it seems (to me) to be a natural progression/emergent behavior of the current implementation of capitalism we subscribe to.
It could potentially be even more axiomatic than that and an unavoidable result of core/firmly held beliefs with trade systems that there will always be those to exploit the weaker (in an economic system) to the point where the system becomes unsustainable.
It often reminds me of agent based models of predator/prey systems where ultimately, the incorrect balance of predators, their efficiencies and successes result in a systematic collapse where the predators starve themselves to death by not allowing the prey to procreate and gather resources necessary that predators ultimately survive on.
In this case, if the wealthy (predators) don't allow the labor force (prey) to collect resources, create value, etc. before snatching added value up ('eating' if you'll humor the idea), they ultimately end up with no future value added from labor force (prey) because the labor doesn't have resources anymore to add value.
From your example following the same basic model, if some of the predators allow themselves to refrain from eating too much and allow the prey to better maintain stable set resources through self control, nothing stops their competitors (other prey) from focusing on their short term gains with no control (yum, more dinner). Ultimately, those predators looking at maintaining a long term stable system will starve if his/her competitors don't share the same views and are allowed to follow the more basic rules. It seems to me, you have to introduce artificial rules into the system to maintain the system (e.g., government regulation or new fundamental underlying rules to the dynamics).
Obviously, the real relationship is far more complex than this view and this model has many shortcomings, but it seems to provide at least some potentially valuable insight to the situation, IMHO.