Precision experiments increasingly target weakly coupled waves, including axion dark matter and gravitational radiation. Such waves are commonly described as classical fields, yet they could exist in quantum states with no classical counterpart. We exhibit two severe obstructions to detecting nonclassical effects, both independent of the mode occupancy. First, realistic detectors cannot resolve the fundamental modes of a field; instead they couple to coarse-grained “effective” modes, which often washes out nonclassical effects. Second, all nonclassical effects are suppressed by extra powers of the weak coupling, making them much harder to detect than the waves themselves. We prove this in general, and explicitly show how the suppression arises for quadrature and number statistics, entanglement, and decoherence. The suppression can in principle be overcome given suitable quantum resources, such as highly squeezed detector states, but the required parameters are far beyond current experimental capabilities. We use the axion cavity haloscope as an explicit example, although our conclusions apply to many ultralight dark matter searches, and rule out proposals to establish the quantization of gravity from observations of gravitational waves.