More concerning than the ecological scar left behind by the eradication of some species of mosquito is the precedent that would be set. Once you've deliberately eradicated one pest species, people will incorporate the knowledge of that action into their image of how the world works and the sort of things we're willing to do. The next time somebody proposes that a species be eradicated, there will almost certainly be less debate.
I've heard people defend the deliberate eradication of mosquitoes by pointing out how we've already deliberately eradicated viruses like smallpox. This demonstrates my concern. What will the eradication of mosquitoes be used to justify? It's already the case in the modern era that angry mobs of idiots need to be restrained from emotional outbursts against animals (https://en.wikipedia.org/wiki/Western_Australian_shark_cull). Having scientists justify the extermination of mosquitoes will only make it harder to get these angry mobs to back down.
I don't really doubt that human-feeding mosquito species could be eradicated without much harm to the environment, but these social concerns remain unaddressed.