LCA Bushings and Other Bushings

Yes I guess it's a carpenter I can see that if you have it straight out in one position as it goes up and down the rod would have to be lengthened in order for the lower control arm to travel in the exact same spot up or down

Yes. The "middle" of the arc would be the "longest" travel. Then going up with the control arm or down would effectively "shorten" the strut rod and that movement would have to be transferred "somewhere". The only place we have now is the LCA bushing. It may well be it's such a "small amount" of fore and aft movement that it doesn't matter. But an arc is an arc.