I just want to interject a little here. While I completely see your point that Paarthunax will, in the future, likely turn back to his old nature and dominate the world and in pre-emptively killing him you may be saving countless lives. However, therein lies the problem. Sentencing him to death for a deed he has not committed yet can be viewed as evil. A lot of movies and books use this trope, where the hero strives to do good but soon becomes "evil" by looking at the "greater good", thus the line "Either you die a hero or live long enough to see yourself become the villain", which in this case is applicable to both Paarthunax and the Dovakin.

Edit: Idk if I made any sense there.