For instance, when center-aligning a triangle inside of a circle, the mathematical center will look visually unbalanced.

I don't know how feasible this is, but would it be possible to construct this feature in such a way that photoshop (or illustrator) would calculate the mass of the selected objects within their bounding boxes, find the average center of mass for each object, then align centers to those points?

The feature would also need to take into account the average center of tint/brightness values, since color sometimes causes the unbalanced look when aligning to mathematical centers.

The same could be said for aligning edges. The feature would automatically calculate the average edge.

I don't know how feasible this is, but would it be possible to construct this feature in such a way that photoshop (or illustrator) would calculate the mass of the selected objects within their bounding boxes, find the average center of mass for each object, then align centers to those points?

The feature would also need to take into account the average center of tint/brightness values, since color sometimes causes the unbalanced look when aligning to mathematical centers.

The same could be said for aligning edges. The feature would automatically calculate the average edge.