Is there any way to "simplify" an existing vector shape layer by somehow "averaging out" curves to remove as much of the unnecessary anchors as possible?
For instance, a simple sphere can be just 4 anchors. The one I'm working with has 100 anchors. The vast majority of them are useless, and only make the shape look uneven upon close (zoom-in) inspection. If there was an option, perhaps one with a slider ever, that allowed me to "simplify" this vector shape by removing anchors and adjusting angles to compensate, it would help me a great deal.
No, not really. But you could try converting the shape into a selection and then back into a shape. This will likely end up with a shape that has far fewer control points, but it won't be perfect and you'll still have to clean things up a bit, but it will proably be easier to move five points then try to remove 96.