Photoshop: Bezier handles on the points in the Curves Adjustment panel

How do you think it is interpolated at present?

Maybe shouting into the void here, but would love if handles were added to the points on curves right now. The automatic interpolation leaves much to be desired. Alternatively, I would love to be able to input a mathematical formula to generate a curve. I am aware of the Parametric Curves filter addon, but it actually produces stepped/coarse results in 16-bit color mode.