You still get bitten, I'd say it would be a bittersweet win.

Correct, but this would only impact the species that bite humans.

Amazing resource here with a ton of info I did not know:

https://www.livescience.com/what-if-all-mosquitoes-died

To your point, yes:

"mosquitoes are a primary food source for numerous animals, including bats, birds, frogs, fish and dragonflies, it’s likely there would be at least some ecological impacts, at least in the short term. Dragonflies, for example, are often known as mosquito hawks, owing to their ability to eat as many as 100 mosquitoes in a single day. It’s likely they, as well as a host of other critters, would, at the very least, have to change their diets somewhat."

To the larger point:

"There are around 3,500 mosquito species, but 'only around 100 will potentially bite and spread disease to humans,'"

So we eliminate the 100 species that bite humans, that still leaves 3,400 species for the bats, birds, frogs, and dragonflies.

In fact, it may not even be necessary to completely elimimate the 100 species that bite humans, kill enough of the biters, and they may evolve into a species that just doesn't bite us.

If you look at the mechanisms of poisons, they all mess up some process in the animal or plant.

For example, Glyphosate is a very effective herbicide. It prevents plants from producing some amino aids. It "starves" the plant.

This has the same vibe as "the bullet didn't kill them, it was the blood loss that got them"