If I remember correctly, Esbern actually gives a decent reason for killing Paarthurnax. I can understand why he wants to kill Paarthurnax as well. Given his position, I may come to the same conclusion. I mean, come on, his name includes the words "overlord" and "cruelty" in it! Furthermore, Esbern recognizes Paarthurnax's role in helping humanity...but also believes that he must atone for his sins. Kind of like how if a man murders a small family, but then proceeds to save the lives of twenty other families. He still murdered a small family. In a way, keeping him alive is a more pragmatic approach.
It reminds me of the story of one "Karla Fay Tucker". She was sentenced to be the first woman to executed in Texas for a long while, a few years back. There was a lot of controversy about it, since she became a born again Christian, and helped people on death row. But her past crimes were extremely gory and vicious. Killing people with a pickaxe, no less. She didn't just outright murder either. She relished in it. She said herself that she actually experienced multiple orgisms while slamming a pickaxe repeatedly into one woman's chest. Like Paarthurnax, she never really defended herself. I give her credit for that. She was resigned to her fate, but would be grateful if pardoned as well.
Needless to say, she was executed. Other parts of the world are even more expedient. They would have executed her right away. But man, so many people raised hell about it. Mostly people who disapprove of execution in general and believe in ideas like redemption. They expect everyone else to believe in redemption too. Maybe they're right. Maybe if they try hard enough they'll change the world. Or maybe they just live in a fantasy world, with values that are irrelevant to the outside world. For most people, it doesn't matter if someone redeems themselves. The victims' family should probably get the only say-so on forgiveness, but they wanted her dead too. I bet if we got like a flashback scene of Paarthurnax in his heyday, at least some people might change their tune. Not all, but I'm sure some would. Essentially Paarth, whoever he is now, gets to live for thousands of years in quiet bliss, while his victims amounted to nothing. Probably humble humans who lived pointless, short lives in slavery, and then got burned to death for nothing.