People always say that you should write your local representatives if you want anything done. Or perhaps you could write to the Governor. Is there any point in writing to judges? The real question being, do judges have any power to do anything based upon "casual" written requests of that sort?
Is there any benefit in writing your local judges?
do judges have any power to do anything based upon "casual" written requests of that sort?
No. Strictly speaking, a judge ought to ignore requests which are not --officially-- part of judicial proceedings. In theory, the idea is to isolate the judiciary from influences that contravene a judge's duty to follow the law. However, the truth is that corrupt judges entertain impermissible requests, and unfortunately those instances are hard to uncover.
Instead, requests to members of the judiciary --and more typically, to the court-- need to be submitted officially. That is done by filing a complaint or suit (for instance, asking for injunctive relief), a motion in an ongoing judicial proceeding, or an Amicus Brief (with its accompanying motion to submit amicus brief) regarding that judicial proceeding.
In motions and Amicus Briefs, the filer or moving party presents arguments premised on principles equity and/or law with the purpose of persuading a court to issue certain ruling. In other words, the purpose is to persuade the court that the proposed ruling is consistent with --or bound by-- enacted statutes and/or legal precedent (aka controlling law) that judges ought to follow.