There's one specific species that causes malaria. Getting rid of that particular one would probably do more good than harm. Their place on the food chain can be filled in by others.
But if they fill in the place in the food chain, that also means they need to be snacking on us.
And I'm not just saying that to be a smart-ass. If humans were a different species, we'd call them horrendously invasive, awful for local ecosystems and that it's really important that their numbers are kept in check, or whatever other euphemisms there are.
No, I don't want to suggest that we should leave humans to die, but we should be aware that it's not as simple as just saving a few lives. We will run into different problems sooner rather than later.
Everything I've read suggests that mosquitoes aren't a primary food source for anything, and that their absence would be relatively easily adusted for by those creatures that do eat them. Still, that's a hell of a dice roll.
Edit: And apparently that may be wrong anyway.
For other animals—such as lizards, frogs, spiders, and other insects—adult mosquitoes are the primary food source.
I have argued for the same caution every single time this came up on Reddit, because I know of a dozen examples in history where we fucked up something similar.
I got downvoted every single time, across several posts over the years, because obviously the hive mind believes things will be different this time! The thing that males me confident it'll fail is I've never seen, and nobody's ever provided, an example where this type of ecological engineering has actually succeeded for the better.
The biggest reason it may be different this time is previously we were all like, "let's exterminate dogs," and it turns out dogs are important. This time is more like "let's exterminate pitbulls." There will still be plenty of mosquitos around if the plan is ever put into motion, we are only targeting a very small slice of them. That doesn't mean there won't be issues, it could well be just as big a mistake as all the previous times. But at least it is more likely to work out.