My thinking is that this goes back to my comment about the 2D plane and the pipe. There is a difference between them, but we would model them in the same way.

Think of it like this: If we had a pipe, how much surface area is in contact with the outside? In comparison, if we took a slice on the plane (to make it look like the point source), we will only have the top and bottom surfaces to radiate. The neighboring slices would also have only the top and bottom and cannot go "radially/axially".

I am more surprised in how SIMILAR they are than the differences. Although it looks like the circle is already approaching a limit and the bar still has a ways to go.