There’s been a well documented population crash cycle of this phenomenon in ecological studies, now called the snowshoe hare-lynx cycle.

Run away populations are not a good thing. Starvation is a hard, slow, horrible death. The cycles of booms and crashes can be devastating and each is a risk that given any additional stressor, one or both of the species may go extinct (even if you’re talking about geographic extinction).

And you’re right. The erasure if sharks would set a great many species, including us, on that cycle. Predation is important for balance.