Delete unnecessary points

Please see this post in the main forum. I am looking for a script (if one exists) that will delete unnecessary/redundant points.

My OP:

Let's say I have a rectangle, and in addition to the corner points, there are extra points along the paths. I want to get rid of these, as they have no purpose. Object> Path> Simplify doesn't do it, nor does Object> Path> Cleanup. I can use Remove Anchor points, but I have to select them all first.

Thanks.