One of the big problems today considering energy is its storage (e.g. batteries are not that efficient, very expensive and polluting). Energy is classically mostly stored as some kind of potential (in a battery, a high-level water tank, ...).
Compare it with the equivalence between a condensator and a coil: a condensator holds a potential energy of $1/2CV^2$ and a coil holds a kinetic energy of $1/2LI^2$. We use batteries to store a voltage as a potential energy, but is there a way to store current (e.g. in a hypothetical superconductor that superconducts at regular temperatures)?
I could imagine one example where kinetic energy is actually "stored", i.e. thermal energy storage (as used e.g. in solar thermal electricity systems). But are there other ways to store kinetic energy, and in particular an electric current? Or is this inherently a less attractive option due to thermodynamics (i.e. due to thermalization the kinetic energy will get useless)?
The question may boil down to: is it inherently physically more attractive to store energy as potential energy, or are we till now just hold back by practical limits (such that in the future we may be able to store kinetic energy in an efficient way)?
*Some context: the reason why I came up with this question is that energy transportation is also a big issue. Energy is of course transported as a kinetic energy (a current through the grid); but if it would be possible to also store it kinetically, less conversion would be needed. Moreover, energy would be stored (in some kind of PEC storage loops) and transported by the electricity grid.*