In the attached image you can see that leader lines have 2 possible anchor points, the vertical centre of the left and right of the text bounding box. Unfortunately, it is not possible for the anchor point to be the horizontal centre of the top or bottom of the bounding box.
Try it yourself by dragging the end of a leader line in a circle around the text it will snap between the left and right only.
This makes for awkwardly placed leader lines in cramped conditions.
For example, if the text is directly above the item to which the leader line is pointing, it will have to go at an angle down from the vertical centre of the text across to a point below the horizontal centre, see next image.
In the above image you can see the results of my suggestion (a line I have had to draw in using the Draw toolbar) where the line has an anchor point at the horizontal centre of the top of the text bounding box.
Can ESRI add one at the top and the bottom to accompany the ones on the left and right?
Microsoft Word and Excel have something like this functionality when you insert a shape:
Their leader line version, however, is a line where you can adjust the position of the anchor and the destination point. This might be optimal for ArcMap too.