Why do people believe Sword is to "reform" the world government? Their only stated goal is to fight pirates who are outside their reach because of internal politics in the Marines/WG. They have never mentioned the Celestial Dragons, slavery, or the atrocities committed by the Marines.
If anything, it's more likely that Akainu created the organization to have a strike team outside the Gorosei's leash they have on him. And he even has a sword tattoo on his shoulder.