Is this not a thing? Is it merely because it's equivalent to a regular buck that has with fewer parts?
Consider the standard inverting nonisolated Cuk configuration:
Consider the junction of the switch and diode: Is + Id is continuous (give or take inductor ripple and switching transients), and positive. (Which, by the way, is fantastic for a ground referenced shunt resistor, for an average current mode converter.) Suppose we ground the output instead (R = 0), and disconnect these from ground, so that Is + Id feeds a new load node (and R_L).
Is this not better, because it has continuous current flow on all three ports (input, positive output, and negative output)?
The key is that C sees full ripple, just as the input cap on a buck, or the output of a boost. It's still not perfectly equivalent, though: C acts against leakage inductance, whereas in the vanilla configuration, you must add an extra inductor for that purpose (say to get a 2nd or 3rd order lowpass response).