Multimodal fusion is the default approach for combining heterogeneous sensor streams in industrial monitoring, yet no systematic method exists for determining \textit{when fusion degrades rather than improves} detection performance. We present an \textbf{Asymmetry-Aware Routing Framework} -- a three-step diagnostic procedure (unimodal performance gap, gate weight attribution, modality corruption testing) with formal decision criteria -- that routes multimodal systems toward the appropriate fusion strategy before deployment. We validate the framework on three datasets spanning two routing outcomes: (1)~the OHT/AGV industrial dataset (thermal + sensors, 13{,}121 samples), where the framework correctly identifies severe asymmetry (gap ratio 3.1$\times$) and recommends \textsc{cascade}; (2)~a chain conveyor fault detection scenario (audio + vibration), where moderate asymmetry leads to a \textsc{fuse} recommendation with positive fusion benefit; and (3)~the CWRU bearing dataset, providing controlled validation in both directions. Threshold sensitivity analysis across all three datasets shows that the framework's recommendations are robust to threshold perturbation, with correct routing maintained over a wide parameter plateau. Comparison against simpler diagnostics (gap ratio alone) reveals that Step~1 alone is ambiguous for moderate-asymmetry cases, demonstrating the necessity of the full protocol for reliable routing decisions.