There would be, certainly. We don't have to eliminate them, though. Just modify them so they can't carry the diseases anymore. Both are options that we could carry out right now, if there weren't checks and balances in place to prevent it. Which admittedly is probably a good thing, since eliminating them would be the easiest thing to do.
I am all for this type of intervention. I do think we should be careful, but this isn't much of a slippery slope. Mosquitoes in particular cause immense human suffering. We've already done untold damage to our ecosystems, why stop now. Nobody would miss the mosquito even if we did decide to wipe it out, and the few species specifically dependent on them would just be the casualties of war I guess.
Yeah, we can genetically modify and release them to breed with the native population. I think some scientists already think they have an actual solution drawn up to do just that for mosquitoes, but, as you said, there's a lot of ethical debate and government concern on implementing such a plan.
That's fully understandable, considering that's where we got Africanized Honey Bees. Granted, it was more hybridization and selective breeding than straight up genetic engineering. It was an attempt to make a more hardy bee that could produce more honey. Turns out, they were just that, but incredibly defensive like their African counterparts, and they broke quarantine and began their march across the Americas, hybridizing existing colonies by mating with the new queens when old queens died.
Oddly enough, Brazil is trying to create a more docile Africanized bee, through the same selective breeding practices that Americans and Europeans previously used to create a docile bee for use in bee keeping.
I think, with the mosquitoes, they went beyond selective breeding and introduced genes that made them safer for us. I can't recall what they did, but they did manage to accomplish it IIRC, and all they have to do is let the males out in the wild (males do not bite), and when they breed with females, the new offspring will carry the same genetic traits.
I think as long as we aren't introducing this method using a highly aggressive species or one that can host even more diseases, then not much can really go wrong. It's not killing them off, just, essentially, taming them.
Frankly, I say just kill off the mosquito species that can survive on blood and blood alone. Leave the rest of the mosquitoes that rely on nectar, who will surely breed to replace the lost population, helping to minimize long-term unforeseen ecological impacts.