A paladin doesn't "purge" anything. You read too much Warhammer.
A paladin is the embodiment of justice. Justice doesn't always come in the form of death. A righteous paladin will only slay an opponent who is truly evil and irredeemable; demons, evil creatures, beings that know nothing but evil can never repent and thus must be eliminated.
But killing a fellow sentient creature without due process? This is not the role of the paladin. Murder is an evil act.
The creator of the paladin class disagreed with you quite strongly:
"A player with a Paladin character asks if this character can put someone to death (who) is severely scarred and doesn't want to live. Although the Sage Advice reply was a strong negative, the actual truth of the matter might lie somewhere else. The player does not give the name of the deity served by the Paladin. This is the key to lawful good behavior in AD&D terms. Remember that good can be related to reality ofttimes, but not always. It might also relate to good as perceived in the past, actual or mythical. In the latter case, a Paladin could well force conversion at swordpoint, and, once acceptance of the true way was expressed, dispatch the new convert on the spot. This assures that the prodigal will not return to the former evil ways, sends the now-saved spirit on to a better place, and incidentally rids the world of a potential troublemaker. Such actions are good, in these ways:
1. Evil is abridged (by at least one creature).
2. Good has gained a convert.
3. The convert now has hope for rewards (rather than torment) in the afterlife.
4. The good populace is safer (by a factor of at least 1).
It is therefore possible for a Paladin to, in fact, actually perform a mercy killing such as the inquiring player asked about, provided the tenets of his or her theology permitted it. While unlikely, it is possible."
- Gary Gygax, "From the Sorceror's Scroll", Dragon Magazine #38 (June 1980)
