CP as an aerodynamic function was abandoned by NACA in the '30s when the existence of the pitching moment was confirmed.
Taking CP to the limit as is needed in manuvers such as a zero lift descent, as Martin Simons explains, results in a CP infinitely aft of the wing.
Once the force moves off the wing, it has no more effect on the wing, if one follows the math generating the CP rigorously.
It's only a mathematical contrivance, and can't be measured in a wind tunnel.
Cm OTOH follows the rules of physics and is a parameter measureable in a tunnel, and is present on every NACA airfoil profile since the '30s, and the modern aerodynamicists also include it in aircraft polars.