The geckos can eat other insects, they are not obligated to eat aedes aegypti. You would need to identify a creature that can't eat anything else, and then justify why humans have to die in order to support that creature's extremely selective diet.
replyWhat's the worst that can happen?
reply The extermination of sparrows – also known as the Eliminate Sparrows campaign – resulted in severe ecological imbalance, and was one of the causes of the Great Chinese Famine which lasted from 1959 to 1961, with an estimated death toll due to starvation ranging in the tens of millions (15 to 55 million).
Though that's unlikely to follow on from simply reducing mosquitoes in urban areas ... it absolutely warrants a close eye being kept on roll out and knock on effects.
The choice is not between making one species of mosquito extinct or doing nothing.
replyThe choice is between making one species of mosquito extinct or using traditional mosquito control methods such as removing standing water. The traditional methods affect many different insects not just mosquitoes. Attacking specifically the species that are vectors for disease is the more ecologically sound method.
If we could remove the insects that carry disease then the outcome could be more insects overall, because people will be more willing to have ponds, etc.