Prosecutions and the mentally ill
It is obviously in the public interest to resolve the truth of the allegations against Lord Janner. But if his mental condition prevents him offering his defence in a criminal trial, then he is unfit to plead.
There are too many cases where mentally ill, or incapacitated, people have been sentenced without proper defence.
This gives weight to the call for some sort of "trial of fact", which would be more like the inquisitorial process of an inquest than the adversarial one of a criminal trial. It wouldn't be able to reach a criminal verdict, or to impose a sentence, but it would provide a judicial forum to determine the facts.