When generating a drawing that includes mesh elements with a lot of facets, the results, while accurate, appear a bit "messy" from a distance. Is there any way to reduce the number of facets for a more pleasing output without inherently changing the mesh itself?
Yes, the Mesh Edge Display tool will allow you to control the amount of faceting displayed on a given mesh element.
This example shows the results on a specific mesh element using three different options. In this particular case, setting the Crease Angle option to a tolerance of 30 degrees does a good job of simplifying the appearance of this mesh in the 3D Model:
And in this image we see a close up view of the before and after results of all three options: