Why does capacitance consume power?

Ideal capacitors and ideal inductors do not dissipate energy, they store energy and release energy like a spring or pendulum. This type of impedance is called reactance as opposed to resistance. Reactance is represented by imaginary numbers, while resistance is represented by real numbers.

Real world capacitors have an Effective Series Resistance (ESR) that consumes a small, usually negligible, amount of energy.