The cost-economics debate around agentic operations has converged on a slogan: cloud is cheaper at small scale; on-premises is cheaper at large scale. Like most slogans about complex economic decisions, it is approximately wrong in operationally consequential ways. The actual inflection between cloud opex and bare-metal capex is workload-class dependent, sensitive to a half-dozen parameters that the slogan obscures, and crossable in both directions over a system's operating lifetime as workload characteristics, accelerator generation, and capacity-sourcing posture evolve. This paper specifies the crossover mathematics, identifies five workload classes with distinct inflection profiles, and treats the cost decision as a governance-layer concern within the HGC³AE² framework rather than as a finance-only or infrastructure-only decision. The argument is that mission-ready agentic operation has a workload mix dominated by classes whose inflection sits much earlier than the cloud-default slogan suggests, and that organizations applying the slogan uniformly are systematically over-paying for cloud opex on workloads that capex amortization would carry more cheaply. This is Paper 3 of the *Managing Agentics Ops* series, closing the foundation triad with Paper 1 (Capacity Sourcing) and Paper 2 (Heterogeneous Compute Routing). The remainder of the series develops operational depth on the substrate these three papers establish.