The equilibrium isn't a conscious decision it's one achieved through food supply/scarcity causing populations to increase and dwindle. It swings back and forth but generally there is an equilibrium.
Generally this falls apart in situations such as invasive species being introduced or the environment is suddenly and radically altered by an upright evolved monkey apex predator.
We did used to find a balance but then we got smart and overpowered and too numerous.
So literally exactly what humans do. (Also your now ignoring that in the quote the animals are doing this "instinctively" not by outside forces like food scarcity so already your arguing its wrong too)
Your describing reality. Humans or any other animal breed until they outstrip the food supply then die off a bit then breed more again and so on, humans just happen to be ableto move goods around. This isn't even mentioning there is no new area to move to humans haven't had a new area to move to for centuries now.
Nothing like the quote.
Shockingly a quite from a 90s Sci fi movie about using humans as batteries is scientifically inaccurate