You have finally answered what everyone has been trying to figure out - why you reject every answer to your question. It is contained below. There IS no precisely defined scenario to give to you that meets your criteria. Some of which you only (that I can see) state below.
Given that you are assuming that the police will ignore the law - any law - and that the court will let them get away with it and convict innocents. It is right there in the quoted section below. And given that the 5th Amendment is a law (supreme law of the land notwithstanding as the police WILL ignore it by your own words below), then NO, there is no scenario where it will make a difference. If the police ignore all laws, and the 5th is just a law, then it does not matter if it exists or not - it makes no difference.
And that gets none of us anywhere. You've simply made it a stupid question that has, by your definition, no possible answer. Congrats.
"All I'm saying is:
Suppose you're innocent the police ask you if you're guilty. With the Fifth Amendment, you can refuse to answer. Without the Fifth Amendment, you would just say "No."
At that point, if the police don't like the answer that you're giving, and if they're corrupt enough, they could just beat you until you confess -- and since that's happening outside the boundaries of the law anyway, the Fifth Amendment doesn't help you. The police will just say that you waived your Fifth Amendment rights and confessed.
For that matter, since the police aren't allowed to beat you, they'll have to lie in court about how the confession was obtained. And if they're willing to lie in court anyway, they can just lie and say that you confessed, even if you didn't. Again, since they're acting outside the law, the Fifth Amendment doesn't help you.
Which brings it back to my original article: To show the benefits of the Fifth Amendment, you need to come up with a specific, precisely defined scenario where the outcome is different depending on whether we have the Fifth Amendment or not. The scenarios that people have been proposing, all fail that test, for the reasons described above."