The current has some limits, but with enough copper you can probably put some serious amperage on it, and a superconductive magnet in "persistent mode" can apparently keep going for months. Not sure how I'd feel about several MWh in a single circuit though.

It might be easier to just build a big flywheel.

Issue with flywheels tends to be containment when they explode, flashing a MWh of metal due to containment failure I would hope to be safer. Additionally a superconductor wouldnt have gyroscopic forces to worry about.

1MWh is almost 1 ton of TNT. If you have that energy in a flywheel or in a electric circuit and something goes wrong, you need containment in both cases.

If the circuit losses superconductivity and a part overheats, it will release 1MWh in a very short time, that will cause an explosion.

You should look up what happened at Cern when they had a superconductor meltdown. And that one wasn't even a burst of power it was a continuous current (admittedly one with enough to power a small city).

Of course anything with that much energy is possibly violent, but at least a flywheel is easy to control. I haven't the faintest idea what that amount of electromagnetic energy would do, I'm not sure I want to find out.

At the very least I suspect you'll find that electromagnetic current also has angular momentum at those scales.

Cern has blocks of metal to contain the heat in these scenarios.

There’s no way to quickly transfer the energy from a flywheel however.

In a superconducting coil there are similar repulsive magnetic forces, which can easily disintegrate the superconducting wire at very high currents.

Therefore the coil assembly must be designed to support the wire and resist to the highest forces expected.

So there are similar problems with flywheels and superconducting coils, in the case when the stored energy densities are also similar.