What is the effect of a per se rule barring the police from a reasonable period of privacy with a reasonably intelligent man who has just been placed under arrest?

We can see no reason rising to constitutional proportions requiring a per se rule barring the police from a reasonable period of privacy with a reasonably intelligent man who has just been placed under arrest and advised of his rights to remain silent and to counsel. The "compelling necessity" of preliminary screening interrogation "has been judicially recognized as sufficient justification, even in a society which, like ours, stands strongly and constitutionally committed to the principle that persons accused of crime cannot be made to convict themselves out of their own mouths." Culombe v. Connecticut, 367 U.S. 568, 571, 81 S.Ct. 1860, 1862, 6 L.Ed.2d 1037 (1961) (Frankfurter, J.).