1. It _really_ _really_ wants to repeat itself and your own prompt, which is antithetical to comedy. The temperature, presence penalty, and frequency penalty parameters _kinda_ help, but when you increase those too much, things start to break in other ways, like you hit an <|endoftext|> before you hit the punchline you were looking for, because the model is trying so hard to avoid repetition.
2. Being just a predictive language model, it doesn't really _know_ you want comedy, nor can you purposefully instruct it to be funny (even in the instruct models). The AI is going to bias towards playing it completely straight.
3. Since it was trained on the entire internet, there's a good chance if you get a funny output, it just "plagiarized" someone else's joke, which can be awfully disappointing when you Google your output to see if that was the case.
4. Sadly, despite the name, OpenAI is very restrictive in their use cases, and they're heavily indexed towards appealing to commercial customers. The playground is still overly sensitive about what it considers "inappropriate" outputs, and their list of disallowed use cases seems longer than the rest of their documentation. It's hard for me to imagine them allowing too many funny use cases of their API, given what I've read on there.