Thanks for expanding and clarifying your comments. I too find much of the U.S. court system troubling; more to the point, the common law itself. The standard catch-phrase in the United States (about government in general and the judiciary in part) is "checks and balances", but those checks and balances often seem quite primitive (most having been designed 100+ years prior to mathematical formalism / rigor). We need checks and balances to be sure, but we also need homeostasis and self-repair; we need a rigorous system of axioms upon which to base logical reasoning; we need a solid philosophical grounding. The very fact that a legal rift exists between so-called Originalism and so-called Living Constitution theory tells me the entire system lacks a formal (rigorous) basis.

Given that the American judiciary grew out of the English colonial judiciary, which in practice looked more towards the whims and largesses of the aristocracy than any principled grounding in (legal, philosophical, or mathematical) form and structure, it does not wholly surprise me.

We do better now than the English colonial judges did, but we can do better still.