I believe I recall reading that if we were to eliminate only the disease carry mosquitoes, those responsible for transmitting maleria, dengue fever, Ross river virus) there ought not be a problem in the ecological web of life as other mosquitoes would fill the void.
They don't feed on people, or they don't feed in general? If the latter, how do they even survive? They eat in their larval form but then not as adults?
Typically, both male and female mosquitoes feed on nectar and plant juices, but in many species the mouthparts of the females are adapted for piercing the skin of animal hosts and sucking their blood as ectoparasites. In many species, the female needs to obtain nutrients from a blood meal before it can produce eggs, whereas in many other species, it can produce more eggs after a blood meal. A mosquito has a variety of ways of finding its prey, including chemical, visual, and heat sensors.[36] Both plant materials and blood are useful sources of energy in the form of sugars, and blood also supplies more concentrated nutrients, such as lipids, but the most important function of blood meals is to obtain proteins as materials for egg production.[1]