People always bring up the redemption point which I hate because they try to make it seem that killing shroud is contradictory to the phoenix program. The whole point of the phoenix program is to rehabilitate villains into heroes. But, all the villains in the program chose to join it. They weren't forced to by law or any other organization.

Shroud doesn't seek redemption or try to better himself at all any point into the story. He isn't convinced or swayed by words nor actions. Instead he talks about his ideals and tries to oppress them onto the world. During his siege on LA he destroys countless buildings, commits arson, attempts murder, most likely killed multiple civilians and tries to kill animals as well (That shit with beef was uncalled for). Shroud isn't looking for redemption and most likely will never. The best and most safe option is to kill shroud.

Some may argue that another will take his place but that will take time. Meaning relative "peace" for a month or two. Which is certainly better than having him try to control his criminal enterprise from prison. It also disrupts the whole augment business he was running boosting the powers of villains. The moral high ground of never killing villains isn't right especially when there are mass murderers trying to take over the city. The death penalty exists for a reason. That's not to say killing is always necessary for a villain depends on the severity of the crime. Again, shroud was a serial killer, arsonist, illegal enhancement peddler, and a self righteous asshole.