Itch mite males get infertile from Neem, except they don't have to get on your body, to impregnate the female... therein lies the issue.
If you feel an itch mite on your body and you can send a puff of Boric Acid powder on it, then it kills it, but it is impractical for most people, even I can't do it every time, after all I won't be interrupted every time something itches.
Itch mites, just like ear mites, can live off the body, and they do. In addition to that they are not killed by laundering, by high temperature, they are very hardy. They don't even drown when you take a bath. The can be brushed off your body, so when you shower, that is what you should do.
On the other hand, their eggs can be washed out easily from the vagina with just water, and you don't even have to go too deep. Just be consistent and regular.
If having a vagina that is functional is of value to you, then please do the frequent irrigation.
One more thing: ginger tea in high enough concentration will kill adult itch mites, but I am not sure yet what is high enough concentration. I will test it later today: I'll stand it the tub and use a cup of ginger tea to rub it all over myself and wait a few minutes. I'll let you know how long, and if it works at all.