Apparently, the only thing mosquitoes are really good at is spreading disease. Anything they do (pollination, serving as food for birds and fish) can be done by other species who don’t bite humans and drink human blood.
And eradicating them entirely won’t cause a global ecocatastrophe.
Ecology: A world without mosquitoes • 2010 Jul 21 • Janet Fang • nature
Genetic engineering has been explored as a solution, by creating male mosquitoes that will inseminate wild-type female mosquitoes whose resultant offspring will be non-viable.
Genetically Modified Mosquitoes Join The Fight To Stop Zika Virus • 2016 Jan 26 • Greg Allen • goats and soda • NPR
But this is going to work on a species-by-species case, and there’s a concern that eradicating one species will just result in another mosquito species occupying the niche the eradicated species did.
(While <p>A. aegypti</p> is the dominant disease-carrying species, there are 41 species capable of transmitting malaria and 4 species identified as carriers for zika)