Hammurabi went hard against people who accused others of serious crimes but couldn't build an airtight case -- which is like the opposite of what we do today. Imagine if cops and prosecutors had to serve the sentences of suspects they charged but couldn't convict.
In medieval to modern times we try to balance this with having high burdens of proof, presumption of innocence, beyond reasonable doubt etc.
In very recent times, the erosion of those values together with the ease of making baseless but effectively ruinous allegations lead to situations where we see ancient Babylonian codes as providing a solution!
Apparently there was an assembly of judges who heard cases. There are strict laws governing judges too; if a judge later reneges on a decision he made, he would be made to pay up to twelve times the original judgement and be disbarred from the assembly.
Yeah, Hammurabi was probably tired of having to constantly adjudicate disputes between clans, so his top priority was probably to shut down most complaints from the get go.
Hammurabi didn't adjudicate things himself, despite popular belief (based on stories about King Solomon?). His kingdom had a panel of judges to hear cases -- and the Code had laws to keep them honest. Apparently, the judges often ignored the code in their rulings, however, indicating that judicial corruption is as old as civilization itself.
But yes, not burdening the judiciary with frivolous trials is as good a reason for a high evidentiary standard as seeing that justice is done and the innocent not unfairly prosecuted. Part of the reason for the infamous Japanese high conviction rate, for example, is because the Japanese system won't bother to arrest or charge you unless their case is very solid.