Is there a default system prompt for the API? Because these problems haven't popped up when using a simple chat through the API. Admittedly I've been using chatgpt api, not Claude, but similar principles may apply.
No default system prompt in the API. There are some topics I much prefer chatting with the API due to system prompt of the web front-end being so restrictive (eg. song lyrics). In general I recommend people to try the API with no system prompt to more accurately see what the default tone of a model is.
There is still some sort of system prompt even through the API. It will still refuse to give you medical/legal/financial advice and so on.
That behavior is baked in the model via RLHF, it doesn't require a specific prompt.