It's a matter of prioritization that you're missing. The founders desired a free state, and understood that the existence of such is wholly contingent upon certain rights of the individual being sacrosanct. It's pretty clear from a reading of the Bill of Rights which those were: speech, press, religion, personal ownership of arms, security of house, home and private effects, right to a trial by jury with representation of legal counsel, etc., etc.
They understood that without these liberties **of individuals** being protected as inviolate (or as nearly so as practicable), a free state could not exist. To attempt to examine the relative worth of the 5th Amendment by evaluating its possible effects on crime in society misses the point...the free society desired by the architects of the republic simply does not exist without it (again, see Abu Ghraib, Guantanamo Bay). Ergo, any utilitarian analysis of this sort is pointless on its face.