I have just reread Old Man Logan and have finally decided to make this proposal I've been planning to do for a long time.
What's The Work
The work is called Old Man Logan, a comic about Wolverine in post-apocalyptic USA 50 years later after villains teamed up and with Mysterio's help almost all superheroes were slayed in one day. With the death of superheroes few supervillains divided USA's territory by areas controlled by them where the law is no more. Hulk's family took control of California and many families have to pay money to keep living in their houses or else Banners will kill them and eat their remains. When Logan's family was left with no money to pay for the next month he had no choice, but to assist Hawkeye in delievering a package in order to gain a reward.
Who is the Candidate? What Has He Done?
Hulk is the head of Banner family which terrorizes California. Once a hero he eventually became a heinous villain soon after the apocalypse has started (possibly due to being driven to insanity by his radiation sickness). After that he forced his cousin (She-Hulk) to breed with him and this union gave birth to Hulk family, a gang of brutal thugs who would go on to bully and terrorize others. Hulk himself bragged about his incestous relationship with his cousin due to her being the only one who could give offsprings to him without dying from his gamma radiation. His other crimes include cannibalism, multiple murders and oppression of innocent people. One day he got bored and ordered his grandchildren to kill Logan's family in order to anger the latter and provoke him into awakening Wolverine and eventually fighting him. Ultimately, this action of Hulk led to his demise by Wolverine.
Freudian Excuse/Mitigating Factors
Hulk has no Freudian Excuses nor redeeming qualities shown. He doesn't care about his family nor other people as he shown no reaction when his entire family except for his remaining son and grandson were slaughtered by Wolverine. In fact he was aware that the latter will go at rampage if Logan's family is killed, but he still went for it in order to fight Wolverine aiming to kill him and feel the taste of life once again. He wasn't concerned that his family is dead because he still had his son and grandson alive and with them he could restore the family and get back at its former activities again.
Hulk does stand out from other villains shown in Old Man Logan. Aside from him, his gang and other thugs encountered by Hawkeye and Logan the other villains were Ashley (Hawkeye's daughter and Spider-Man's granddaughter), Kingpin and Red Skull. The first two were brutal criminals who only aimed to control their area and Ashley after killing Kingpin have succeeded in doing so. Red Skull is an already known PE villain, but in Old Man Logan he didn't have much things shown aside from tyrannical rule of Washington. Hulk on the other hand was the final antagonist of this comic who had the most atrocities shown and all of them were heinous, which indeed makes him stand out from other villains.
Ultimately I can say that this version of Hulk definitely meets all the criteria required to qualify as Purely Evil villain. He comitted heinous atrocities, doesn't care about anyone, has no reedeeming qualities and stands out from other villains in the work.