It is a frequent matter in the transitions of power that those falling from power are dealt with with death or exile or imprisonment so that they don't attempt to resume any form of power/division. It is just as frequent that ambitious loyalist take opportunity into their own hands as the two men today have. The new leader David had no such desire and saw through the career climbing initiative of the two plus he had an oath with his now deceased friend Jonathan to spare him and his family.
Again it must be noted, the context of the Bible must be judged also in the context of the times. Modern readers judge David and Israel as being war hungry and blood thirsty. We have this notion that offensive military maneuvers are unjust. David praying to the Lord "shall we attack" and the Lord being for and ahead of that battle seems to us harsh and alien. The context of the time suggests rather that this offensive battle tactic was quiet common in the time, it can be described as attack or be attacked. Add to this that Israel is a land that has been taken from other peoples, people much greater in number than the Jews and that the Jews are riddled with divisions and idolatries, signs of weakness to any other aggressor. The question others might have is more on the lines of God has been with Israel undoubtedly but for how long? God is using this type of natural inquiry to test Israel's resolve and trust.
2012 - pBiblx2 Field Wise Bible System Version 2.0.9d - GPL3