We are in agreement about how kindly old Judge Earl Warren came up with Miranda out of that. But, he used that and other amendments to tell the police that if they had someone in custody, and that if they wanted to question him about a crime so as to able to use those statements as evidence at trial, then they had to give him the Miranda warnings.
Almost every police show depicts an officer handcuffing someone and immediately reading the Miranda rights. That is not a good procedure to follow, because if he invokes, the detective who might want to question him is screwed.