I touched upon in during Impel Down, but I think there's an argument to be made for executing Ace for his actions as a pirate. We've seen very little of him over the course of the series, but during his initial introduction in Alabasta he extrajudicially killed a bunch of Baroque Works minions, and while fighting Blackbeard helped destroy a town without second thought, possibly killed innocent civilians who weren't able to flee. Those are two very tiny examples in a long pirate career that undoubtally ruined a bunch of people's lives. You can argue about the morality of capital punishment, but it seems firmly established in the One Piece world. I don't doubt that if Ace didn't have the father he had, his actions would still rise to the level of execution.
But Ace isn't executed because of his actions as a pirate. If he lived the life of a saint, the World Government still would have hunted him down. They tried before he'd ever been born.
This is the World Government's sin. It's been thematically established since Enies Lobby that existence is not a crime. Whitebeard and the marines are not fighting a war over the life of a single pirate, but as Doflamingo states later, the right to define what is Just. It asks, should the Powers that Be be allowed to target people for the blood that runs in their veins, or should people be allowed to live freely as children of the sea, regardless of their heritage.
While it might initially seem like the WG wins this confrontation, their victory sows the seeds of their own destruction, while powerful piratical forces like the Straw Hats only grow in influence.
