I think the important thing to consider is no one should be above the law. The laws that exist have been made and passed for a reason.
However, heroes are far from perfect. In order to protect the innocent and save the world, they have to break several laws. Some might say that makes them criminals as well instead of just vigilantes, but they are needed since they can accomplish things the regular law enforcement agents can't and are unable to given the restrictions of society.
Superheroes do have abilities and the willingness to go above and beyond but as citizens of the city, state or country they operate in, that doesn't mean they can do whatever they want. If it was truly believed heroes have the right to take matters into their own hands, wouldn't a superhero exemption clause be officially passed?