The clearest example is prewar Virginia where there was direction competition between free and slave labor. The free labor outcompeted slave labor at growing tobacco, which is why people expected slavery to die out on its own. Then the cotton boom caused Virginia plantations to switch to growing slaves.
You also make a theoretical argument. At most that suggests that the landowners should earn more. That is not the same as production. Moreover, free people put most of their surplus into growing the next generation of free people. Empirically, free populations expand much faster than slave populations.
Why does this work? Why does adding new bodies of water save you from the mosquitoes that were already breeding in the old bodies of water? My first thought was that if you add 10x as much water area, then 90% of the eggs will be laid there. But you explicitly say that if you treat big bodies of water, the mosquitoes will still breed in small bodies, which seems directly opposed to this strategy. Maybe this only works in a narrow range of conditions, but you might as well try it.