Female mosquitos mate once and only once. When they mate with a sterile male, none of her eggs will hatch.

Several insects are like this. In the species I'm familiar with, the male member breaks off inside the female locking all other males out.

Releasing sterile screwworms in Panama has been the main method of protecting US beef/cattle production from the insects spreading north out of South America.

https://www.pbs.org/newshour/nation/what-to-know-about-the-n...

Penicillin used to kill 100% of Staphylococcus aureus. My point still stands - even if a selective sweep takes out 99% of the population, they will recover.

This is at best a temporary solution.

The remaining 5% and their adapted mutation will eventually repopulate the local population.