Rebuilding Curves to be SubD friendly - never symmetrical

Why are the rebuilt curves never symmetrical? They are practically worthless when the input curve is intentionally symmetrical but the output curves never are.

How large is the deviation from symmetric that you see?

I did a simple test and found a deviation from symmetric of 1.e-07 which is probably the result of accumulated round-off error in solving for the interpolated curve.
RebuildSubDSymmetry.3dm (1.9 MB) That small a deviation should not cause any problems.

Post an file with an example if you see something different.

A basic example, bottom closed curve (spline) rebuilt to above with subD friendly on, same number of points (10). Completely wonky.

A polyline rebuilt SubD friendly with the same number of control points (24). Completely wonky and asymmetrical.

Upload a .3dm file with the before and after geometry.