Did any of the Four Imams assume the role of a judge, and what was the reason for their refusal to do so?

None of the four Imams assumed the role of a judge. Rather, they refrained from drawing near to kings and from taking on judicial positions, fearing to fall into what the Prophet, peace and blessings be upon him, warned against: "Whoever is appointed as a judge has been slaughtered without a knife." Many scholars, however, did assume the role of a judge when it became incumbent upon them.