(Yes, if we used more hydro-electric then that would do the job for us, but it's not the case that we need this in order to store energy).
But your main point is correct. This has to store energy to control frequency.
This all becomes more complex when the loads are switch-mode power supplies and the generators are solar panels. The flywheel project adds some smoothing to the grid, as spinning generators are replaced with DC devices. But the principles are the same; without any extra devices, electricity has to be generated at the exact instant that it is consumed, and the consumers have a large physical effect on the generators.
(Frequency is not proportional to voltage in general, only in this spinning-generator connected to a spinning load case. You can obviously switch DC on and off at whatever frequency you desire, and a perfect on/off cycle consists of infinitely many frequencies at various amplitudes.)