They're not about to come turn around, come into a court, and admit a mistake. It's unrealistic to expect that. Governors very infrequently use their pardon or clemency powers. They might do it for a very minor crime, say, maybe a 25-year jail sentence for selling an ounce of marijuana. It's rare to see a governor pardoning or granting clemency to a person who's been convicted of a horrible murder.
Governors have the same political considerations as prosecutors, maybe even more so.
Families, lawyers, and maybe some media care about wrongful convictions. But prosecutors and governors don't want to project concern about criminals. Some prosecutors would agree with me, and some would not. Some prosecutors are so righteous, and so convinced of the defendant's guilt. But I think a lot of people would agree with me.