There are a number of issues here, and you are focusing on one, while ignoring many others. That's the real problem with taking these types of incidents and trying to writ them large and draw a conclusion that you believe will fix the entire mess.
First, a lot of times the prosecutor drops the charges because the Police made procedural errors that would mean that the accused baddie would walk ten seconds after the court case got started. It isn't political any more than anything else. It is a result of laziness and attitude of the police most of the time. They just don't want to be bothered doing it right. We are talking about the Chicago PD that had a secret jail where people were detained, questioned, coerced into confessing, denied legal representation, and then lied about it.
if you are going to win at Baseball, you have to follow the rules. If you are going to win at Football, again, you have to follow the rules. Following the rules is the key to victory in every sport. When you break the rules, you are penalized, the more serious the violation, the more serious the penalty. In Automobile racing, if you car does not meet the standards of the rules, your victory will be taken from you and awarded to another. You can get a horse to run faster by using various medications, and then have your horse disqualified because of it. You can run like the wind, and lose the race because of performance enhancing drugs.
Our court system is set up like the aforementioned sports officials. Judged, referee's, and experts scrutinize the play to make sure that no one is cheating. The Prosecutor presents the case, and will argue it if you follow the rules before they get involved. If you broke the rules, then who is going to stand up and argue that it's not fair you have the victory stolen from you just because you cheated a little bit?
Next is plea bargains. These allow people to plead guilty to a lesser crime and have the larger crimes dropped as part of a deal. There are a lot of folks who say that these are good because they free up valuable court time, and take a probable winner and turn it into a definite win. There is no telling how the Jury will react to the case. How many times have we all seen a pretty obvious open and shut case tossed out by the Jury? You can mention OJ Simpson, and there are a lot of other examples.
Plea Bargains give the Prosecutor a victory, and the Defense wins because the accused is not facing fifty years. Nobody wins it all, each win a little bit.
Yet Plea Bargains are often used in what seem to be egregious violations of law, where multiple felonies are wiped out by a minor misdemeanor. The accused pays a minuscule fine, does a few days in jail, or a few weeks of community service, and the case is done.
Finally we move to jail sentences. Jails in large cities are normally overcrowded. Remember Lindsey Lohan? She was sent to Jail, and a few days later was out with time served because of overcrowding.
Depending on the crime that is finally agreed to in the plea bargain, chances are the accused will have time served long before the case actually gets to be agreed to.
Each step in the process has to be done right. It can't be short circuited, or skipped. You can half ass it as a cop, or a prosecutor, but then the defendant goes free because of your errors.
Chicago has one of the worst reputations for the Police Department. The place where criminal cases actually start. Many of their cops have been caught lying on reports, or under oath. Many have been caught breaking those rules, and when they are, and aren't fired, or prosecuted themselves, that makes every case that comes after fodder for the defense.
Let's say that Officer John Smith is a cop, he was caught lying about the probable cause for a search before. Now, he's a witness for the prosecution. The Defense calls the Prosecutor and says I'm going to really go after John Smith, so if you don't have a lot of video that John did it the right way this time, I'm going to fight to get the evidence suprprssed and if I fail I'm going to tear him a new ass on the stand during the trial.
The Prosecutor doesn't want to lose either, they don't want to get embarrassed before the Judge, and they look at the evidence. There is little or no video evidence to support the statements of John Smith, who was caught lying on the stand previously. What do you do then? Do you go forward and let the defense attorney rip John Smith a new ass on the stand? Do you hang your entire case on John Smith's word? What can you say to the Jury? I know he's lied before, but he's telling the truth this time.
Now, you may feel that this isn't fair. The idea that the prosecution has to work so hard to put a criminal away may be outrageous to you. But our system was set up this way. Criminal cases are held to a higher standard, the idea that the person is guilty beyond a reasonable doubt. The prosecution has to follow the rules. The cops have to follow the rules. If they skip a step, or lie about it, or if they have a history of doing either, then that reasonable doubt gets easier to have. If the skipped steps or halfassed efforts are too big, or numerous, then the Judge will just throw the case out, which is what he is supposed to do.
It isn't that the Prosecutor is a Democrat, or the town or city is a democrat. This happens all over the nation, all the damned time. Republicans as well as Democrats do the same thing. Chicago is infamous and perhaps worse about it, but it starts with the cops. A mistake by the cop early on will screw up everything that follows after.
I honestly believe the old quote. It is better for a hundred guilty men to go free than one innocent man be convicted. I believe that is a good standard, because incarcerating an innocent man is a heinous crime, one that can never be undone.