The fifth amendment is really just a recognition of the fact that a person will not give reliable testimony under such circumstances anyways. The idea behind this is sound, and actually is a refinement of the judicial system, and understanding of the fact that people will avoid telling the truth about wrongdoing in most cases, making their testimony largely irrelevant.
There is more to it than that, but if you remove the fifth amendment protections, all you are doing is saying 'I will condemn you for not talking, even though there is no way to verify independently that you actually have anything to say'.
The question is a suggestive question. The Fifth Amendment does not protect the CRIMINAL, it protects the innocent from arbitrariness of the ruler. The protective effect of the 5th Amendment for real criminals, as suggested in the question, is lower than in other states. Defendants in Europe do not have to swear an oath and explicitly have the right to lie in court.
The fifth amendment is a key component of our justice system. It is not a weakness but rather a strength. It forces the state to prove its case rather than to twist a defendant's words to make him look guilty. Even an innocent man could made to appear guilty by a clever prosecutor.
No, I do not believe that the Fifth Amendment protections for criminals weakens the American justice system. I say this because if a prosecutor does not the evidence to convict a defendant without him or her incriminating themselves, then they do not have a case. If a person is guilty there should be sufficient evidence to convict without any doubt.
The idea behind the Fifth Amendment to the U.S. Constitution goes back to the Magna Carta. History has shown that government and individuals of authority within the government can often abuse their position of power. The protections set in place may help criminals from time to time; but, without the Fifth Amendment protections the potential for injustice becomes very real.
No the 5th Amendment does not weaken the American Justice system it just tells us that the person knows more than what they are willing to share at the time of their trial and that they won't disclose what they do know. When they are protected everyone in the situation is protected.