Anti-sodomy laws are not enforced. So how are they going to avert the cost you allude to?
Such laws cannot be practically enforced within the confines of the home, and that's perfectly fine. There are many, many laws that cannot be effecvely enforced within the home. Mutual assault and battery is by far the most frequently committed crime in the home that cannot be effectively prosecuted.
BTW, "consensual" sodomy (in the home, out of it, . . . who cares where?) by an AIDS carrier can result in a death more painful and hideous than any torture devised by man. To a lesser extent this is also true of anal gonnorhea and hepatitis B. Of course, now that we spend more taxpayer money on AIDS research than the other top three diseases combined, we've been able find, fund, and distribute a cocktail of drugs enables sodomizers to again indulge their perversion relatively freely--at taxpayer expense, of course.
To do away with such laws wholesale by fightening people with threat of bogeyman "bedroom police" which have never existed and never will exist, is disingenuous at best. It's a bald-faced lie at worst.
When we eliminate the laws wholesale in the idiot belief that we must be open-minded and tolerant, the only message we send (or that is heard) is "Party on ,dude! Someone else will clean up you mess later for you!"