God must have had some good reason for creating mosquitoes.
By God I mean the Deist, Philosophy God, not necessarily any of the Theist, organized religion God(s).
I know that fish eat mosquitoes. So do frogs.
We would be depriving the fish and frogs of their food supply if we annihilated mosquitoes.
The mosquitoes do however kill more humans than any other animal does including man himself.
Various species die out all the time and the Earth seems to survive though.
And mosquitoes killing people may also serve as a population control.
Back in my motorcycle days I have eaten my share of mosquitoes in the early morning and late evening when they come out. They don't have much of a taste, so you would need to add salt and pepper. The fish and frogs must not care then.
My instinct would be to kill them, sure. But I am trained to kill things. It is a natural bias that I have. All thanks to Uncle Sam.