Catmull-Clark subdivision, which TC and most specialised subD modellers use, raises facet count exponentially. A smesh sphere with 14 x 14 divisions, 196 faces, blows out to 44.8K faces at level 4 smoothness. TC isn't like specialised subD modellers because it's got a CAD kernel, with a processing overhead that pure mesh subD modellers don't have. SW has a Modo plugin, you don't build entire models with it, you use it to create dress faces. The criteria for a subD mesh in mechanical CAD is that it looks smooth if the resolution of the mesh is below the resolution of the machine being used to produce it, so you'll use a different smoothness level to suit the scale of the object. That's also hugely ignored in rendering: what's the resolution of your render going to be? Print or online representation? 96 d.p.i used to be regarded as "web" resolution, but with 4K screens showing up on laptops, that's not going to be pretty.
There are plenty of free subD modellers that will subdivide an object quickly if you want to test whether that'll give you a better render. Blender, which is such a subD modeller, has two rendering engines, and one of those, Cycles, is also built into Rhino and Poser as their native renderer, although you can throw money at VRay and Flamingo and plenty other renderers, too.