Yes; fuck them.
We (intentionally or no, mostly not) cause the extinction of hundreds to thousands of species every year for much more mundane reasons: deforestation is the big one, climate change another. And that buys us arguably nothing but enriching people that benefit from the process of deforestation and climate change--folks that're economically desperate enough to log illegally, and energy barons. These extinctions are mostly tragic, and the net benefit to human societies is likely negative.
Mosquitoes are fucking evil. They kill more humans every year than any other animal. Malaria is only the most well-known disease they spread; see also dengue ("breakbone fever", named for what it feels like), West Nile virus, and more. Those that malaria doesn't kill are frequently left with a low-level chronic infection that makes them less effective as people. Malaria and mosquitoes kill children, disable the working population, and economically cripple entire nations.
As best we can tell, things that eat mosquitoes also eat other things. But I'd vote for nuking the mozzies from orbit even if that weren't the case. They're such an unmitigated cause of human suffering and hardship.
Considering even today somewhere around 700k people a year die from Mosquito born disease, with many more crippled from lifelong malaria infections, and the total number of deaths is though to be somewhere around a billion through history?
[https://www.who.int/news-room/fact-sheets/detail/vector-born...]
Nuke ‘em