::An infinitely long rigid body with gaussian mass distribution. Are you joking? You wrote that there's "plenty of physicists" who "consider lines and planes of material points, even in mechanics". If there are so many, then you have a lot to teach to those who are interested in this discussion. Can you give some examples, explaining what is the body and body property modeled with a line or plane, and what is the purpose or application of the model? That would be interesting. And if you have an example in rigid body dynamics, that would surprise me, and make your contribution much more interesting. Otherwise, you will never convince me.    
 ::What you are trying to do is  
  provided a model that might be used, that's not enough to convince me.