I hope the Amazonian frog doesn't depend too much on mosquitos as food. Or that by eradicating mosquitoes, insectivorous animals don't eat more of other, less abundant and fast-breeding, insects as a replacement and it starved the Amazonian frog.
(I don't know what the Amazonian frog eats; my point is that biotopes are complex and second- and third-order effects need to be monitored. That's why smaller interventions - e.g. making humans poisonous to mosquitoes, pushing them to the evolutionary path of avoiding humans - would be better than whole eradication.)
Human-biting mosquitoes aren't necessary for the ecosystem and we should remove them.