What are the pros and cons of insect birth control through sterilization?

That is absolutely a loaded question. I consider myself to be a moderately intelligent person. However, I have never seen a cockroach, no want too, I don't know how one would sterilize a mosquito. So I just can't get my thinking around your question. Would you please explain where you heard this theory.

Well, tickle... have you ever seen moth balls? They're pretty small but if you use tweezers you can see them with a magnifying glass.

Actually, pest control methods that use "insect growth inhibitors" (chemicals that prevent the targeted bug from reaching maturity and the ability to reproduce) have been very successful for controlling specific pests. The introduction of sterilized bugs into areas that have infestation problems can work better (and ecologically cleaner) than chemical treatments. If Mr. Bug meets Ms. Bug and they unite... well, whatever they call it... and they can't have "Buglettes"... all they get is a good time and they become the end of their family tree.