TIL many female insects mate only once in their lives. Insect populations can be controlled by releasing flocks of sterile males into the wild. Females mate with them, never give birth and simply die.
From what I've read I get the impression that eliminating biting mosquitoes wouldn't have much impact - there are lots of types of mosquitoes and supposedly few are of the biting kind, and at the same time the ones that pollinate or are food for other animals are usually not a significant source of food or pollination, and the ones that do pollinate don't pollinate anything important to us according to a random article I read. So basically for it to matter you would need to be eliminating a kind that bites and makes up a majority of the pollination or food for something else which seems unlikely.