Its not easy to protect someone from themself. You can’t seriously say it’s the cops fault that he injured himself. That is ridiculous and is not what it means by protecting someone in custody.
Yes it does. That is why they have suicide watch in jails and so forth. Once in custody, the prisoners safety is the responsibility of the arresting authority. That’s why they take your belt and shoe laces. No different than a child under custody by an adult, when in custody, you have no right to free will.