You are mistaken Ned re strict liability.

Yes, minor traffic offenses have strict liability.

Statutory rape is not strict liability. Although mistake or lack of knowledge of minor's age is not a defense to consent, the State still need to prove that the accused knowingly had intercourse. The pubic policy is to protect Lolita from herself.

Re homicides, there are different levels of mens rea: intentionally killing someone, recklessly killing someone, criminal negligence, ....

There are also recognized defenses to killing someone: justification, self defense, defense of another; extreme emotional distress (reduces murder to manslaughter) plus mental health defenses to include insanity.