Phantom Non-Identifiability: When Simplifying a Coupled Simulator Fabricates an Observability Boundary

Reduced simulators are the substrate of physics-informed surrogates and simulation-based inference, and identifiability and optimal-sensor analyses are increasingly run on the same reduced model. We show that a reduction which severs the only path from a parameter to an observed field does not merely lose accuracy: it manufactures a structural non-identifiability that the real system does not have, together with a confident prescription to buy an instrument the real system may not require for identifiability. We demonstrate the mechanism in full on coupled heat and moisture (Luikov) transport, where dropping the thermogradient (Posnov) coupling makes a Fisher analysis declare the moisture sensors blind to the temperature-side parameters, and an E-optimal step prescribes a temperature channel. Restoring the term collapses the null: sensitivities grow as $O(\mathrm{Pn})$ and the Cramér-Rao bound as $O(\mathrm{Pn}^{-1})$, which we derive and use to predict the crossover from one probe solve. Critically, the failure is silent over a wide window: the calibrated reduced model passes a $\chi^2$ goodness-of-fit test while still reporting rank $2$ and "buy a temperature sensor," and it is not confined to inference. The same severed path zeros the input-to-observable Jacobian, so a controller built on the reduced simulator pays up to $12\times$ the matched controller's closed-loop cost while the objective component its own model treats as controllable improves. A frozen parametric PINN inherits the phantom, and a two-head control rules out the obvious confound. We give the criterion that identifies the failure in other reductions.