The Judiciary has had a somewhat shaky past...
I feel something needs to be there to make sure the rules are followed properly to maintain order, and this is the role the Judiciary is intended to fill.
The issue in the past (as I've seen it) is that it's been used against people who make honest mistakes.
ie. a new comer who opens up a save and plays ahead without realizing that it's not allowed. The new comer is likely to apologize for their error when they realize it's not permitted... however a investigation and sentencing still proceeds despite the fact it was a minor error and the person is apologetic.
Another issue is different interpretations of the law. The Judiciary is intended to help resolve these differences in interpretation. But again it is often taken too far.
Two people read the constitution and come away from it with two different views of what it means because it's hard to address every way someone might interpret a clause. Somebody, with a full knowledge of the constitution may honestly feels an article allows them to do something, when someone else may feel that action is forbidden by the constitution. The result of which should simply analyzing the law and determining what the proper interpretation should be as a group (ie. Public Poll) and clarifying the wording, and continue on with the game. Instead, it gets turned into an investigation into the individual and sentencing process to determine what "punishment" if any should be given to the "accused."
95% of all issues brought before the Judiciary should not result in any finger pointing or discussion of possible punishment. But I saw it happen far too often when I was playing.
The remaining 5% is for when someone knowingly breaks the law for one reason or another... intentionally ignoring valid instructions, intentionally ignoring the will of the people to make sure the game goes the way they want it to regardless of what the citizens want. This is what the "investigations" and "punishments" are intended for... but there's still a problem.... How do you judge "intent" of someone who you never see or hear? How do you "prove" it's an honest mistake when all you can offer is your word? The problem is you can't.
The Judiciary is intended to try to prevent the demogame from delving into chaos, by ensuring that everyone knows the rules. For that reason it can't simply be ignored otherwise chaos may arise if an issue arises.
Also, to be clear I'm not saying the Judiciary needs to be structured like it has been traditionally (to me a "simple arbitration mechanism" is just another type of Judiciary), in fact I think there's definitely room for improvement given the amount of finger pointing in the past and the length of investigations that can clog down the demogame. However, whatever mechanism is used to resolve such issues of rule breaches and interpretations it needs to be in place beforehand to ensure the process of deciding how to resolve those issues does not in of itself bog down progress.
Edit: I think this quote is appropriate for the Judiciary discussion...
It is better to risk saving a guilty man than to condemn an innocent one. - Voltaire