Why would releasing sterile mosquitoes help erase the population? Do they eat each other or something?
It works better than trapping & killing.
I once heard a modified version of the plan, where you release male mosquitos with a "driving Y chromisome" - that is, a Y chromisome with a mutation that leads to male offspring. Supposedly this should spread in a population even when but eventually leads to extinction.
There is obviously the question of whether it would be sufficient, in time - the figures around time-frame were surprisingly short - but that's not a solid guarantee. Even if it just produced a substantial collapse for a couple years, it might help substantially in fighting malaria, though.