> they're generalist eaters
Humans are also generalist eaters. That doesn't mean there won't be severe problems if you suddenly eliminated, say, all rice crops.
> genetic solutions involve releasing some form of male mosquito that can sterilize eggs ... Most transgenic things can't maintain the foreign gene for about 10-20 generations
Setting aside that your description is a bit wrong but probably just mixed the words up... how exactly can an any mutation - artificially induced or otherwise - that results in sterility be inherited "for about 10-20 generations?" The whole point is the females, who only mate once, will waste that chance mating with a modified male and thus prevent any future generations. The genetic modification used for mosquitos involves a mutation that prevents the larvae from reaching adulthood, meaning there is no second generation of modified genes, let alone 10-20 of them.
> So the solution would involve releasing male mosquitoes to fertilize the eggs that sterilize females in the eggs
This is not at all how the mosquito lifecycle works. Not even close.
Adults mate with adults. Males mate repeatedly, females only once. A single modified male can therefore prevent maybe four or five females from laying viable eggs, 100-200 at a time multiple times in their life, which is about a thousand eggs in total depending on the species. The females are not "sterilized in the eggs" - they're not sterilized at all. Their eggs will hatch but the offspring will never mature into adults.
=Smidge=