If you're fine with the risk of a possible ecological disaster, then kill them all off. But remember, killing all the wolves was also thought to be a great idea at one time. Fortunately, we weren't able to achieve that goal before discovering we were wrong. Such decisions are final and can't be undone if they go wrong.

The hubris is in the idea, that with such a long human track record of being wrong about such things, is executing a such total and final idea is the right thing to do. But go ahead and do it. I'll be safely dead when the error might be discovered.

The amount of ecologically horrifying acts that our species has already done, I'd be willing to add "got rid of mosquitos" to the pile.