Mosquitos are important food items for many species of birds like swallows and purple martins, bats, and especially dragonflies, which are the mosquito hunters of the insect world, and as such, form an important part of Earth’s ecosystem.
As for “why can’t we get rid of them?”, it’s because we as a species don’t want to badly enough. We could basically nuke every potential mosquito habitat with a wide array of pesticides and habitat modification, if we wanted to (think “paving and/or draining the entire state of Florida, then dousing it with insecticide”), but the tradeoff would be the poisoning, ruination, and total desolation of Planet Earth, since many other species would also perish, all the way up and down the food chain.
Seems kind of a steep price to pay for a few skeeter bites.
I suppose someone could, if they wanted to, come up with hormone-based mosquito control the way they came up with flea control and roach control, but as mentioned, mosquitos are an important food item for many other species here on Planet Earth. If you were to spread some kind of mosquito hormone control around your scenic pond next to your house so you can sit on your deck in the evenings without being eaten alive, all your barn swallows, and the martins whose house you so carefully put up, will move elsewhere, as there’s nothing for them to eat. You also won’t have any dragonflies after a while, but not everybody cares about that.
And since mosquito larva also constitute an important food item for fish, pretty soon you’ll start noticing that you don’t seem to have as many sunnies in your pond as you used to…
Calamine lotion works well, BTW. Shake the bottle really well for a couple minutes, dab it on with a cotton ball, let dry.