Pretty sure Anthropic and other providers prepend these "official" system prompts to your conversation even if you send in a custom system prompt otherwise it would be trivial to produce CSAM, etc.
Any mention in the system prompt is mostly defense in depth, and to make refusals more graceful.
If the prompt were the only protection, it would be extremely easy to produce illegal content after a long session.
But how do you start a Claude Code session without a system prompt?
Otherwise DANmode and similar jailbreaks would still be as easily accessible as they were at the beginning.
afaiu they have other systems for denying and re-routing requests