I don't think we should eliminate any species but unfortunately we are. Biodiversity is part of what makes the ecosystem stay in balance and work properly. The near extinction or extinction of many types of frogs, bats, bees, elephants, rhinos, condors and other species is difficult to personally watch. I believe part of the mosquito issue could be stemming from the lost of habitat for those species that help keep them under control and changes in climate.
We don't experience much of a mosquito issue where I am at but there are many frogs in the waters around here and not many larger animals.
Yes, human activities have always affected the animal kingdom, if not directly, then indirectly at least. But mosquitoes are a real issue and this is one species I wouldn't 'miss' if they were gone!