It's true that getting rid of mosquitoes won't bring peace between humans and insects. But it would help, and if we could make them extinct then we could avoid all the collateral damage that occurs due to our efforts at partial suppression. Insecticides do more harm than the insects they target do good, so if we could target individual species for extinction (obviously a technological feat, but within the realm of possibility) we'd ultimately have a more diverse and healthy ecology.
"At field-realistic levels of pollution, neonicotinoids and fipronil generally have negative effects on physiology and survival for a wide range of non-target invertebrates in terrestrial, aquatic, marine and benthic habitats"
Fact is, removing insect biomass using neonicotinide insecticides has had major negative impacts on North American biodiversity.