Thought experiments can be powerful, or they can mislead. Einstein came to his Special and General theories of relativity* by considering such questions as "What if you were traveling at the speed of light and looked in a mirror?" or "What if you were traveling at the speed of light and looked sideways at a beam of light?" As seeing is dependent on light bouncing off the object and hitting your eyes, what does it even mean? Of such impossible what-ifs a lot of science is generated, but also a lot of history, sociology, business management, mathematics - even the arts. Okay, in the arts it can get seriously crazy.** Yet these reimaginings can also be illuminating and useful. Science fiction and other speculative fiction is built off such ideas as "What if these robots started developing some group identification, or ethics?" "What if our concepts of fairness were introduced to a planet where 90% of everyone is dies before the age of five?"
With that in mind, consider the following. In the English common law tradition, a person is considered innocent until proven guilty. This derives from Biblical, Greek, Norse, and Roman sources, and is not universal to mankind. It is not even universal in those lands it descends from, as it goes against the grain of human response to injustice. Our natural tendency is to avenge, not to wait, and even in places where there are procedures for gathering evidence there are mobs, secret societies for revenge, and social destruction in the court of public opinion. As Americans (and Englishmen, Canadians, etc) we have internalised the idea of innocence, of starting from zero even when there is obvious evidence to the contrary, but even we are not that good at it. Witness, for example, our political discourse. There is not a lot of wait-and-see, partly because we know that the first theory that gets to the imagination has an anchor effect on what people will believe forever. Life ain't fair, and the percentage of people who believe the NPR/TPM/HuffPo myth about Jared Loughner and Sarah Palin's website is depressingly high.
I have had a theory passed along to me - from a person who doesn't accept it but thinks it worth noting - that in regards to sexual crimes there is even more division on this. The energy is higher, tempers are shorter, the leaps to conclusions are longer. Other traditions could easily have weakend this idea, and in particular, centuries of societies in which women had more power might well have concluded that punishing dangerous sexual behavior was just as important as the presumption of innocence. That would seem at present an insult, that women just don't get the abstract idea of presumption of innocence the way men do, the silly things. However, had that been the case we as a society would likely not feel as strongly about that particular abstract point. We might well accept that errors on both sides would always be with us, but group comity was important. As I noted above, we already do feel that way much of the time, men and women both. String 'em up.
Presumption of innocence has worked well for African-Americans and other minority groups over the years, enough that Thurgood Marshall believed that the Civil Rights protests were needless endangerment of you blacks. Until there is victory in the courts there is no victory at all, and he believed the court victories were proceeding nicely, with nobody getting hurt. The insistence on abstract principle has guaranteed freedoms and safety that would likely never be won at the ballot box. Yet the cost of so many criminals, from rapists to petty thieves, getting away with crimes is not negligible. It is a horrible thing for an innocent man to be put in jail, but it is also a horrible thing for an innocent girl to be unavenged. I think our principle is correct, but it does come at a cost.
Campus accusations of sexual crime illustrate this separation. In this societal subgroup where women now have more power, the preference for punishment of perpetrators against women over the protection of the accused has shifted. It has also bled over into whether people should be able to say things in public that upset other people. I don't lay this entirely at the feet of women - there is a sort of male who sides with women on these issues (perhaps in hopes of getting laid - oops, did I actually write that?), and they have been powerful on this score as well.
Let me add in two offsetting things to contemplate, as a thought experiment or three. Our current system has the added benefit of restraining the police and the powerful from just accusing whoever they like and being able to put them away, because the standard of proof would be so low. In the short run that is always a high cost - the police are often very aware of exactly who is guilty - but in the long run it is a gain. The police and the powerful, just like all of us, quickly fall prey to temptations, and quickly start doing whatever the hell they please. On the other hand, the presumption of innocence also has a cost. All of us, especially criminals and those who have weak internal controls, adapt to the environment that says people will seldom be caught, and this encourages all of us to behave more badly. We respond hugely to incentives and disincentives. Most criminals aren't that smart, yet get away with many crimes before they are caught. Serial killers tend to be more crafty, and can go on for a long time. They don't get caught, so they risk more.
Before you think I am wrong, consider the posted speed limits. Or following less than four seconds behind the vehicle in front. Or about twenty other things that we mostly do just because we want to and believe we hardly ever get caught.
Genetics and Incentives explain just about everything.
*You would think the General Theory would be the easy one to understand and the Special Theory to be harder. It's the opposite.
** I saw this when I was two years out from being a theater major and was amazed that someone had dared expose this idiocy, in a movie right out in front of everybody. It was only a slight exaggeration of people I had known from 1971-75. I don't think you could have a scene making fun of that idea nowadays.