It's selective justice. Imagine driving down in a 2009 Toyota Camry with your well dressed family on a well paved highway in Alabama at 78 mph in a 65 mph zone on a nice, clear sunny Sunday a safe distance away from the preceding car at the same velocity as quite literally every other car in every other lane you see. Clearly not posing a safety threat, not lane-weaving indicating any form of compromised faculties or dangerous behavior, no threat at all really. However, Smokey the Bear state trooper Bob decides he doesn't like the way you look. You could be black, you could be wearing a Ralph Lauren Polo with a NORML insignia on it and Bob just happens to hate pot, you could have an atheist bumper sticker and Bob just got on shift after a rousing sermon from Pastor Jedidiah. Justice imposed on selected individuals is not justice.
Ethically, were he to enforce the law to the letter with an egalitarian approach, the first person he saw as he got on shift exceeding 65 should have been pulled over. As soon as that ticket was issued, he should have done so for the next person, ad infinitum until he was off-duty.
In actuality, if every single arrested individual stopped one day and decided to exercise his or her constitutional right to see his day in court like that prep school[1] individual did, we'd see what would amount to be a DDoS on the system incapable of handling a caseload of such magnitude. Pragmatically, an ADA will use a very effective method - known colloquially as "charge stacking" - to intimidate the accused into pleaing out a charge he would likely beat[2].
Though I'm totally with you on the classist component - should Michael Jordan's son commit a crime, he'd be far less likely to be convicted than whitey-mc-Kentucky-Meth-Mouth Tim's son due to the same lack of resources afforded to him.
[1] RE: your rape scenario -- Compare this aggressive attorney http://edition.cnn.com/2015/08/28/us/new-hampshire-prep-rape... vs these less fortunate
https://en.wikipedia.org/wiki/Central_Park_jogger_case
[2] Even more compelling is the motion for dismissal those defense attorneys could raise in aggregate on 6th amendment grounds. In the state of California, the 45 day cap could be breached fairly easily if all of the defense attorneys concurrently suggested to their clients to enter a not-guilty plea. You'd also see a marked decline in arbitrary traffic stops, as arresting officers would be forced to spend the day in court rather than in speed traps.