Recent simulations provide the energetics of ion adsorption at the air-water (a/w) interface: The presence of the ion at the interface suppresses the fluctuations of the capillary waves (CWs) reducing the entropy and displaces the weakly interacting water molecules to the bulk causing a reduction in the enthalpy. Here, we provide atomistic simulation-based evidence that the inferences of the existing studies stem from considering a small simulation volume that pins the CWs. For an appropriate size of the simulation system, an ion at the a/w interface enhances the CW fluctuations. Furthermore, we discover that the characteristics of the waves governing these enhanced CW fluctuations ensure a significant decrease in the pressure-volume work causing the enthalpy decrease, while the same wave characteristics of the CWs become responsible for an entropy decrease. Overall, the paper revisits the free energy picture of this fundamental problem of ion adsorption at the a/w interface.