I think that the left and some right liberals (libertarians et al) tend to want to use the government to assuage their broken consciences. As I mentioned in my posts about the problem of evil, we have what I believe is an innate feeling of oughtness. Not just about the world but about ourselves. Both the OT and NT tell us that the law is written on our hearts. Everyone knows they are a sinner. Having some authority above them give its blessing to their sin makes them feel better.
Why for example do homosexuals, the vast majority of whom are non-monogamous, do not want families (as sick as that is) not settle for being merely left alone, but desperately want the State to marry them? I can totally understand that they want to not be criminally prosecuted for their sins. I cannot understand, outside of my present point, why they care so deeply that the State provide its imprimatur of acceptance to their lifestyle.
Perhaps so much the same for prostitution, drug and other behavior crime advocates. Obviously there is an element there of just wanting to avoid arrest etc. But I think they are also motivated by a desire to feel as though their errant behavior is legitimate. After all, we implicitly understand, like it or not, that the gov't is a sovereign authority.