I disagree. When I look at the diagram it looks like you will be forever adjusting the tension in each cable, only to find it affects the others. While it's not too hard to cope with two cables coming to the same point, once you add the third, it might be a royal pain.
The tension in the cables is normally maintained by a rigid position in space at anchor point. Tighten one cable against a rigid anchor, and it won't affect the other cable because it didn't move (well, maybe the tower moved a bit - getting a pipe tower to look straight when you look straight up is an art) A chain, as you suggest, is free to move around - it describes an arc around the anchor, and the balancing point is wherever it finds all 4 forces in equilibrium. That's a lot of variables to adjust simultaneously.
For example, after you have the upper one all tightened up, you can find that tightening the lower one makes the top cable even tighter, and the middle one loosens. So you back off the top one and then as you tighten up the middle one more you find that the top one loosened up even more...