*Background:*  
I found that it is very easy to use a linear depth buffer, using only a slight modification to the canonical vertex transformation. The simplest method is found at the bottom of https://www.mvps.org/directx/articles/linear_z/linearz.htm.

However, the caveat is that it only works for triangles that don't need to be clipped against the near or far planes. (And an alternate solution, of dividing the perspective divide in the vertex shader, will yield a similar problem for the other four frustum planes.)

Because clipping requires linear interpolation to work across all four clip space coordinates, I think it's impossible to work with linear depth, using  only a vertex shader. But the reason for that is all down to Z being divided by W.

Why is that done? X and Y need to be divided by distance from the camera, but the Z coordinate does not, to fit perfectly into the NDC box.