Aedes aegypti are container breeders, you can totally eliminate them from an environment through diligent removal of standing water left in buckets, tires, pots, etc. This has been done before but the effort wasn't properly sustained so they've made a major comeback in disease prone areas. Killing a lot of them does have a substantial effect because they don't easily travel long distances by themselves so if the remaining resistant population is small enough it might just as easily end up dying out due to its breeding cycle being interrupted through other means. The part that should be criticized here is that any eradication campaign should also involve efforts to eliminate their breeding environments by removing junk and unattended containers that collect water.