The gravity wave drag parametrization of the Whole Atmosphere Community Climate Model (WACCM) has been modified to include the wave-driven atmospheric vertical mixing caused by propagating, non-breaking, gravity waves. The strength of this atmospheric mixing is represented in the model via the "effective wave diffusivity" coefficient K_wave. Using K_wave, a new total dynamical diffusivity K_Dyn is defined. K_Dyn represents the vertical mixing of the atmosphere by both breaking (dissipating) and vertically propagating (non-dissipating) gravity waves. Here we show that, when the new diffusivity is used, the downward fluxes of Fe and Na between 80 and 100 km largely increase. Larger meteoric ablation injection rates of these metals (within a factor 2 of measurements) can now be used in WACCM, which produce Na and Fe layers in good agreement with lidar observations. Mesospheric CO₂ is also significantly impacted, with the largest CO₂ concentration increase occurring between 80-90 km, where model-observations agreement improves. However, in regions where the model overestimates CO₂ concentration, the new parametrization exacerbates the model bias. The mesospheric cooling simulated by the new parametrization, while needed, is currently too strong almost everywhere. The summer mesopause in both hemispheres becomes too cold by about 30K compared to observations, but it shifts upward, partially correcting the WACCM low summer mesopause. Our results highlight the far-reaching implications and the necessity of representing vertically propagating gravity waves in climate models. This novel method of modelling gravity waves contributes to growing evidence that it is time to move away from dissipative-only gravity wave parametrizations.