Scenario: You have been set up by someone else to take the fall for a murder. They stole your gun, used it to shoot the victim, and then put it back. Realizing what had been done, you chose to hide the gun because all the evidence would unfairly point to you. You don't know who did it and have no evidence to prove what happened. The prosecutor asks "Do you own a gun that fires this type of bullet?" followed by "And where is that gun located?"
Without the right to silence you are left in a scenario where you'd be forced to either commit perjury (by saying you don't know where it is) or provide evidence that you know will be misleading to your own detriment. If the prosecutor could use your refusal to answer as a point against you, you could be convicted anyways.
Your FAIL 3 applies, but the condition itself FAILS on several counts:
FAIL 3 is flawed in that it implies that acquitting a guilty person is equal in "wrongness" to convicting an innocent person. I do not believe this to be the case, if for no other reason than that a guilty person can be later caught and their punishment enforced, but an innocent person cannot be "un-punished" and have their lost freedom or life restored.
It is additionally flawed because it would prevent any laws that hamper investigation work for the protection of innocents. By applying your same logic in other circumstances we would have to allow the police to shoot at anyone they want, since the immunity from being randomly shot is equally beneficial to both criminals and non-criminals. We would also want to strike the 4th amendment (since it lets criminals hide stuff as just as well as innocent people), and then we'd want to look into many other situations.
To boot, your supporting statement about a law that hampers all investigations equally being equivalent to deciding guilt by random choice is some sort of logical fallacy, but it's so illogical I'm having a hard time classifying it; it's some terrifying love child of a straw man, false dichotomy, faulty cause/effect, and slippery slope argument. It's so wrong can't even really argue against it except to point out that protecting some percentage of all people from conviction is in no way equal to randomly punishing all people regardless of guilt or innocence, since in the first case innocent people are still safe but in the latter case they have an equal chance of being convicted when compared to a guilty person. It falls apart further from there, but the point has been made.
Shoddy logic here man, and it undermines whatever legitimacy your argument had to begin with.