Spinning metal is just one way to store energy. As long as you have:
- an energy storage system, and
- a quickly-responding means to couple it to the grid,

you got the Schwungmasse. It's considered synthetic when the energy isn't stored in angular momentum. So, a battery storage plant would be a synthetic Schwungmasse.

So would be a solar plant running under-capacity, since its inverters can react very quickly to changes in demand.

In principle, renewable energy is not a problem in itself - but its high utilization is. A solar plant running at 50% capacity may not be very economical to operate, but it sure has quite a bit of equivalent Schwungmasse as it can double its output on the scale of one half-cycle.

With renewable sources running at full capacity, their equivalent Schwungmasse is zero, more-or-less. That's the source of the problem. A thermal plant running at full capacity has same Schwungmasse as an idle one, since the stored angular momentum does not depend on the load at all. It's constant.