Sounds good, but afaik only a few mosquito species actually are spreaders of diseases affecting humans. I suppose I don't know if those pathogens can mutate to use other mosquitoes as hosts. While we're at it, get rid of ticks.
+chiggers
Other prime candidates:
Pediculus humanus (human louse, including the head and body subspecies).
Pthirus pubis (crab louse)
Onchocerca volvulus (causes river blindness)
Trichomonas vaginalis (causes nasty vaginal infections, and can be carried and spread by men)
Ascaris lumbricoides (giant human roundworm)
I believe all of these are parasites specific to human beings, and find it highly unlikely that wiping them out would cause any significant ecological catastrophe.
Those who disagree would be welcome to serve as hosts a fallback population, so we could restore them if it became necessary. Concerned about Aedes aegypti mosquitos? Sign up to serve as a blood donor for them. You can help save the species, at the small cost of yellow fever, dengue, chikungunya, and (apparently) zika.
What, that doesn't sound like a good deal? Then why are you willing to wish that fate on others? Especially unwilling others?
Sorry for any sarcasm, but it's quite disturbing to see First Worlders condemning Third Worlders to horrible deaths because of ecowhacko "concerns" about friggin' mosquitos.