This has nothing to do with intellectual property law.
The reasoning you stated as to why the police need a warrant to search a phone isn't correct, so your attempt to analogize it to you searching your son's phone doesn't really make sense. And, in any event, the Fourth Amendment (which is where the requirement for warrants comes from) doesn't apply to private citizens.
Whether your state's privacy laws have anything to say about the subject is impossible to determine because you didn't identify your state.
General rule of thumb: If you don't own the device, don't do anything on that device that you wouldn't want the owner knowing about or seeing.

