Idempotency is what bites me most in practice — I've been driving these against an unreleased database I work on. The main trap is using the op_id as the idempotency key rather than a business key the client reuses on retry. When they're the same thing, the checker is trivially true and the test passes without testing anything.
No-lost-ack is conceptually the same shape with a simpler property (every acked write shows up at the end), but it breaks the same way most checkers break — if the recorder treats timeouts as success or failure instead of "unknown," real lost writes silently disappear.
Recovery after partial failure is where the AI-agent angle gets shaky honestly. Quiescence is the hard part. Agents will declare a system "recovered" while compaction is still running in the background. The skill forces a three-part check (no in-flight ops, no pending background work, replicas converged) before the invariant runs. How reliably that holds up against a specific SUT, I'm still figuring out.