Frantz Schmidt's father was an executioner, so Frantz didn't have a lot of choices. The profession put the whole family in the hereditary category of "not respectable:" not quite "untouchable", but it was hard to find spouses for the kids (who couldn't get married in a church), you'd take oaths of service separately from everybody else, and you can probably guess some of the rest. Unless somebody needed medical attention--the executioner was also generally a healer as well.
Healer? Well, the job also required the occasional enhanced interrogation, and that gave the man a certain knowledge of anatomy and the limits of the body--and he was expected to make sure that the convict was healthy enough afterwards to undergo whatever the sentence might be (generally something simple like a caning). But that doesn't explain all of it--executioners were famous for being doctors too, and by Frantz's estimate he worked on 10x as many healings as punishments (and most of the punishments weren't executions)--of the order of one a day.
In fact, in his letter to the emperor requesting that the family status be restored, he wrote that he regarded healer as his vocation. The letter and successful reply were preserved.
So was his diary, on which the book is based--together with Nuremberg official records. Early in his career Frantz decided to be as respectable as he could, eschewing some of the vices common to the era and to executioners--like drunkeness (fortifying yourself to inflict the punishments?)--and was an exemplary public servant.
It will not surprise you to learn that parts of the book are a bit grim, and the author's presence is sometimes a bit intrusive (I grew weary of "he must have deeply felt his low social standing"). But the author makes it clear that the criminal justice system of the era wasn't as callous as it is portrayed: there was room for mercy, and a strong emphasis on repentence. Family and guilds could plead the cause of a murderer, and youths got lenient sentences—whipped, compelled to learn a trade, banishment, and so on—unless they repeatedly offended.
Roving bandits were a threat to people outside the city walls, plague paid visits, and eventually wars started coming by. The "archers" were the city police force--generally a motley and crooked lot. Imprisonment wasn’t one of the usual punishments. The society wasn’t as rich as ours, so they went in for more immediate and varied punishments. It was, the author explains, a complicated time for punishments: the customary laws were being replaced with more centralized codes defining the crimes, procedures, and punishments—and they didn’t have all the bugs worked out.
However, I suspect even opponents of the death penalty might cheer one of his executions (mercifully reduced to beheading): Friedrich Stigler, who had taken on the profession of witch-finder. The Nuremberg authorities were not persuaded by his accusations, and convicted him "on account of having given rise to all kinds of unrest, false suspicion, and strife among the citizenry as well as various superstitious, godless spells and conspiracies and other forbidden magical arts and methods elsewhere." It's a pity more German cities didn't follow their example.