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.
The Innocence Project and other anti DP organizations have a vested interest in proclaiming many of these folks as "innocent" when they are nothing of the kind.
Usually it's a problem with a reversal on a technicality years after the offense, when memories have faded and witnesses have died or disappeared. The DA can't prosecute because he can't prove his case 10 or 15 or 20 years after the fact, and that's proclaimed as "innocence" when it's really lost evidence.
The DNA is not the be-all-and-end-all that it's proclaimed to be, either. All that proves is that somebody else was around to leave DNA at the crime scene . . . you can't prove a negative.
This is not to defend in any way the crooked cops and prosecutors and crime labs that cook up fake evidence. Prosecute them all until their ears ring, they contaminate the system. If a few of them went to prison that sort of nonsense would stop immediately.