... the dynamic crosshair does not "actively change where your shots are going," how did you get that impression? Your shots fly in a line out from your gun. This line does not project out from your camera; it projects out from your gun. Therefore, for the crosshair to accurately depict where your shots will go when you are in third person (and, to a lesser degree, in first person), it must move away from the dead center of the screen and towards your gun, as you get closer to a target.
Having a totally static crosshair when your aim is not, in fact, totally static relative to the camera, means having a crosshair that is an approximation or a guideline rather than an accurate depiction. Which would be sort of fine, and probably has its pros and cons, if not for, as you said, the fact that the static crosshair isn't even accurate when you're standing still.
The dynamic crosshair gives you a good sense of "where your shot will hit," but since you have to lead your shots a lot, and are frequently not going to be pointing at your target, I will agree that in a lot of contexts it doesn't really help. I think the best theoretical route would be to have a static crosshair that always shows where your shots would theoretically go if there were no obstacles, AND draw the dynamic crosshair to acknowledge the actual hit location. Drawing both crosshairs like this would imply your "firing line" really well, which would be really cool.
edit: given that it's a third person shooter AND doesn't use hitscan "point and click" client-side weapons, the crosshair design and nature of aiming is more complicated. You need to have a good sense of where you're looking AND where you're firing from, you need to have a good visualization of the line between those two points. Honestly, I think that between watching/understanding how the crosshair jumps around as it passes over targets, watching how your shots fly, and keeping track in your head of where you were aiming and how you're moving, it's possible to keep great track of this line with the current systems.
there's just the other quibble of certain crosshairs (dual pistols) being inaccurate at very close and very long ranges, and crosshairs in general obscuring vision at long range. I don't know what perfect solution i'm wishing for that would let me aim at people at long distance without mostly covering them with my crosshair. Firing each shot as a twitch shot works pretty well, though. Maybe I'd like an option where as you hold down the fire button, your crosshair fades out, allowing for better control/observation of sustained suppressing fire.