Why are two cameras mounted in paralle in stereo application?
When you say cameras are parallel  it only means that the center pixels are parallel.

Every pixel has a different angle, and that refers to the overlapping regions you were talking about. Actually there is at most one overlapping voxel (3d pixel kind of) for every 2 pixels!

There is more about it in epipolar geomtry , it's interesting and pretty simple!