Esarhaddon had a different way to punish "the guilty soldiers who plotted to make my brothers rule over Assyria." He admits: "I killed their children." (Esarhaddon 1 ii 8-11). He deemed this punishment sufficiently severe (kabtu) for their heinous crime of not supporting him.
But Esarhaddon was actually not next in line for the throne, his brothers were. At least one of them, however, had assassinated his father in order to claim the throne, only to be out-maneuvered by Esarhaddon. In a military coup it is seen as important to kill the old guard. The soldiers might have been loyal, but had the misfortune of having been loyal to the wrong side.