The problem is when new predators, especially widely adaptable ones such as coyotes, are introduced into an ecosystem where the prey animals have no defenses ag

The problem is when new predators, especially widely adaptable ones such as coyotes, are introduced into an ecosystem where the prey animals have no defenses against them, they tend to outcompete everything so the populations of prey animals decline and local predators end up with less food causing both populations to decline until only the invasive one is left. This is why introduced and invasive species of both plants and animals are a huge problem around the world. They stifle local biodiversity and you end up with monocultures.