Is it time to downgrade witness evidence?

I was listening to the radio the other day when former newspaper proprietor Eddie Shah was describing the trauma of being put in the dock for something he didn't do, based solely on the evidence of another person. Even if the witness is not the alleged victim, time and again we see cases that are far too dependent on witness evidence. In science there's a saying 'data is not the plural of anecdote.' We don't accept something as scientific evidence just because someone claims to have seen it. And yet witness evidence in court is nothing more than anecdote. And there are very good demonstrations that people are hopeless at providing accurate accounts. Witness evidence stinks. I give a very strong example of this in my book Extra Sensory:
On December 4, 1901 there was as a horrendous incident during a seminar on criminology at the University of Berlin. As Professor Franz von Liszt gave his lecture, one of the students interrupted to give an alternative viewpoint to the professor’s “from Christian morality.” A second student jumped up and disagreed profoundly. He said that he was fed up of with these Christian morality arguments. The first student was incensed. He pushed the desk over and strode over to his opponent, pulling a gun from under his coat. There was fight, the two students wrestling for control until the gun went off. The second student fell to the floor, apparently dead. 
Not surprisingly, the rest of the class was in shock. Von Liszt picked up the gun and asked for attention. He apologized, telling them that he had staged the event in order to perform an experiment. He now wanted everyone present to write down exactly what they had seen. Still shaken, they all obediently wrote out witness statements. And here’s where it gets interesting. The versions that the students gave differed wildly. This was no distant memory and featured no ordinary everyday event. They were giving their recollection of something amazing that had been seared on their memories just minutes before. 
When the different reports were compared there were, for example, eight different names given for the person who started the fight. Across the observers there were wildly differing accounts for the duration of the event, the order in which things happening and how the whole scene finished with von Liszt’s explanation. Some were convinced that the gunman had run from the lecture room – which he hadn’t. He had remained standing over the body. 
The point von Liszt hoped to make – and in which he was successful far beyond even his own expectations – was to show just how unreliable witnesses are when giving evidence in court. And it is totally bizarre that we still place so much faith in witness evidence in trials today, given the clear example of this and many other similar psychology experiments since. Witnesses are terrible at getting the facts right. They really aren’t good enough to rely on in court. Interestingly von Liszt found that the inaccuracies were worst when describing the events that were most dramatic – those, for example, involving the gun. It’s as if the unexpected nature of the event makes us particularly bad at recalling exactly what happened.
There is inevitably an unfortunate outcome of deciding that witness statements unsupported by other evidence is unreliable, which is that it is pretty well impossible to progress any trial based solely on the account of the victim. Yet surely we shouldn't allow innocent people to go through the whole traumatic trial process and potentially be found guilty merely to make it easier for those who don't have corroborative evidence?

When I first heard about the Eddie Shah case I thought he should have the right to sue his accuser for damaging his reputation. After all, if he is innocent, then his accuser is lying. And maybe that still is the case. But a more important outcome should be that this kind of trial is prevented from happening in the first place. Witness evidence alone is simply not good enough. Anecdotes, however forcefully put, will never be data.

Image from Wikipedia