To paraphrase in a different way, but agreeing with you, is to have a label leader that acts more like a polyline in a geometric network were the end stays centered on the label center and the other end points to the feature. But it would need to be offset from the label so as not to interfere with the label. The way is is now is the number one reason I do not use leaders with labels. For those spots where I need to offset the label I created a label feature class as a point feature. I place the point where I want it and then draw a leader to the feature. I then offset the label from the point and give it a rotation for precise placement. I can then change the leader to bend and twist. Would not work for thousands but fortunatly I only have 400 or 500 locations where the offset label is required.
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