The problem with this is that when a total scumbag is convicted for a crime they didn't commit, it means that there is another scumbag who got away with it.
Interesting bit of trivia on this point: As Governor of Texas, George W. Bush commuted the sentence of exactly one condemned man to a sentence of life in prison. The man? Notorious serial killer Henry Lee Lucas. Despite being linked to dozens, if not hundreds of murders, Lucas was convicted of a mere eleven killings and sentenced to death for only one, a yet-unidentified Jane Doe known in case files only as "Orange Socks" (the sole items of clothing her body was found wearing). In a strange twist of irony, later investigations determined that this single victim, Orange Socks, was most likely killed by someone other than Lucas. Faced with these findings, Bush really had no choice but to commute the sentence.
Lucas would die in prison of heart failure a couple of years after his commutation while the true killer of Orange Socks has yet to face justice. The important point is that had Bush not exonerated Lucas for this single murder, the case files on Orange Socks would've been closed. Crime solved. Lucas did it. At least today her file remains open and while the chances of her killer being apprehended are slim, there's still a chance that justice may eventually be served.
Your points are well taken, and I disapprove strongly of the (great deal less common than it used to be) practice of picking out one of the “usual suspects,” framing him, beating out a “confession,” and then closing the case.
My point is that while this practice has highly negative side effects, as you point out, it is not really an “injustice” to the chosen perp, in a cosmic justice sense.