The origin of cosmic structure is widely regarded as quantum, yet the Universe today appears classical. Standard lore attributes this to a "quantum-to-classical" transition on super-horizon scales during inflation. Gravity plays a central role: super-horizon dynamics squeeze quantum states, while the cosmological horizon enforces a system-environment split, leading to decoherence. But are these mechanisms always sufficient? We revisit this question, identifying assumptions and limitations in conventional arguments. We highlight recent work showing that beyond slow roll, non-linear dynamics of cosmological perturbations can generate and amplify quantum coherence at the closed-system level. Preliminary results further suggest that, for the minimal irreducible contribution to decoherence coming from stochastic kicks at the coarse-graining scale, the rate of coherence generation can outpace the decoherence rate. This raises the possibility that signatures of a quantum origin may persist in cosmic structure. We propose a phase-space analysis based on the Wigner function as a concrete route to identifying and probing such signatures.