Mites
Spider mites are food for a variety of larger, predatory mites. Many mites from the family Phytoseiidae, including dark-colored lady beetles (also known as "spider mite destroyers") feed on spider mites. Other predator mites include minute pirate bugs and big-eyed bugs. If spider mites are completely removed from the ecosystem, these mites that feed on them will be affected and run a risk of dying out.
Lacewigs
While annihilation of spider mites and the mites that eat them might be good for your allergies, your house plants and help you sleep better at night, total eradication of these tiny creatures would continue to have consequences for other animals higher up the food chain. Lacewigs, for example, are beautiful insects that grow to about 1/2-inch in length and often camouflage themselves to blend in with the leaves they spend so much of their time around. Lacewigs are one of the biggest natural predators of mites. Other mite predators include black hunter thrips, sixspotted thrip and dusty wings. If you get rid of spider mites, eventually, you'll hamper these insects as well.
Bats
Besides being the only mammals capable of true flight, bats are fascinating creatures which occupy an important spot in the ecosystem. Seventy percent of bats feed on insects, including lacewigs. By ridding the world of spider mites, the ripple effect will be felt up the ladder to bats, seventy percent of which will experience decreased food supply as the insects they are accustomed to feeding upon die out as a result of losing their food source - spider mites and mites. While many humans may feel uncomfortable around bats, they are important consumers of insects and without bats, humans may experience more discomfort from common pests, such as mosquitoes, 1,000 of which can be consumed by a single brown bat in one hour.
Hawks and Owls
Raptors like hawks and owls are predators of bats. If bats were to begin to die out due to a diminished food supply, hawks and owls would find their own food supply diminished. Even some fish are known to eat low-flying bats which skim water surfaces hunting for insects. It doesn't take long to see how eradicating an insect so tiny that it can rarely be seen with the naked eye, has consequences that reach up the ecosystem to higher level mammals. While a few plant leaves might be greener, many other species could be adversely affected by the upset in the natural food chain order.