Most of humanity's best art, literature, music, and comedy is about people experiencing trauma. Being able to joke amidst suffering is the very thing that makes us human. It's also a critical part of empathy itself.
People experiencing trauma writing jokes about it and being able to joke about it despite the trauma can result in great material. The humor provides a shared way to process the traumatic events.
However, it is very different when a third party is doing the joking - and poorly at that. It often ends up just making fun of people who are suffering - which isn't exactly good taste. It is no longer joking amidst suffering, but joking about suffering.
Humor being about trauma is kind of a vague categorization. It's probably more insightful to drill down more specifically.
In this case; this AI is not really trying to convey anything meaningful. It's just regurgitating distasteful jokes that hurt people that are currently going through a tough time.
Generically and universally decrying punching down is extreme and would require spying/policing everyone to implement.