Don't most switching voltage regulators (except the low-current switched cap variety) already use inductors/transformers as the main energy storage element between the rails? Don't the capacitors mainly filter switching and ripple currents?
Using inductors to store energy for digital circuits sounds challenging. Digital circuits require currents in spikes at the switching instants and inductors are not the ideal tool for this. The Ldi/dt drop in inductors will cause additional voltage drops and may not be suitable for digital circuits.