Re: Mutah [temporary marriage] -- Social and cultural perspective
Wrong, prostitution wasn't banned from day one. The prophet began his campaign to free women from prostitution by first making people recognize that these women were humans and not to be treated like donkey crap. In Medinah, in the early days post-migration to Medinah, he found that many men would sleep with prostitutes and then not pay them. So he began by first getting these men to pay the prostitutes.
After it was established that you should give a prostitute enough respect to pay for her services, it was slowly weeded out of practice by placing bans on prostitution. It was a slow process because he coupled the ban with lessons on taking care of the society's women and orphans. Therefore, if you see a prostitute on the street, it is not enough that you throw her in jail and lock her up. If you failed as a society to provide for these women in the first place, such that they're out prostituting themselves, then society is in the wrong by their approach. All this was a gradual weed out process.
Same weed out approach was used for alcohol and slaves.
There is much to "muta'a" that we might not know. Was it reserved for those men who were fighting battles and away from their wives for long periods of time? Was it used as a tactic to taper down prostitution by making men enter into a marriage of sort with a prostitute rather than making it a one night stand? Regardless, considerable evidence shows that it was banned at one point or another and any conflicts in the literature, I suspect are due to forces who wanted to keep the practice around so they could manipulate it.