Poser's group editor has a button to apply a Perspective UV Map, which distorts the texture in the way you would expect. It made me wonder, since Poser has that function, does it have a method to apply a basic cubic or spherical UV map to items that come without one or come with a poorly mapped texture? My thought was the Material Room, but if it's there it is buried real good and called something else.

I'm not looking to learn UV Mapper to design maps to stretch over different shapes. Just to apply a basic overall map where there is none.

The free edition of UVmapper will give you a basic map very easily. 
It doesn't take much learning to get to that point. 

Just load the OBJ, pick Box for a box or Spherical for a sphere,
and then re-save the OBJ file.

These maps serve quite nicely with Poser's simple shaders like Noise or
Weave or Spots or Water.