Evidence is evidence. If you claim you saw someone you know throw a brick through a car windscreen, the cops would investigate but what happens when the accused says that yes he walked past the vehicle and it was OK then but he didn't do what you claim he did? The cops try to find some evidence to back up your claim but find nothing.

What do the cops do then? They'd say there's no evidence to prove what you say is true so there'd be no charge in that case.

So, when you have these historic claims, why do they name the accused and put them through a trial when there's no evidence?

The balance of probabilities is not evidence and isn't recognised as such.