1- Regarding the question on punishments, yes Islam does want to avoid punishing people. Hence, when some offenders would confess the Imams would try to dissuade them from doing so. But if they kept insisting, then at the end of the day they had to be punished. As for believers punishing, this only occurs when all the conditions are fulfilled. If the crime is proven, and there is just no way out, then the offenders have to be punished. If people know there is no punishment for their violations, they won’t be deterred, they commit sins openly, and society becomes immoral. By threatening to punish people for immoral acts, Islam is actually protecting good people from being corrupted. So this is more of a deterrent. In practice, it’s very rare for it to happen.
2- Regarding Mut’ah, my assessment is that most men when put in a position of power they use their position to have a relationship with women. This applies to all humans, whether Muslims or Christians, atheists or Buddhists, Sunnis or Shias, and whether through Mut’a or other means. This same broadcasting company, let them do a documentary on churches and Sunni mosques and you’ll see similar things going on there, although in different forms. So this is a human problem. Men have very powerful sexual needs, and many times they fail in restricting this need. So honestly it’s not a Mut’ah issue in my opinion.
Having said that, not all religious leaders abuse Muta’ah. There are many who don’t but maybe we don’t hear about them or the spotlight is not about them.
Also, Mut’ah has its conditions. If you want to better understand how it works I recommend you see the following classes I gave at our Hawza years ago:
If you have any follow up questions feel free to ask.