If your neighborhood only needs 50MW of power, but you want 1000 MWhr of storage (~20 hours at full power), a Redox flow battery would be able to do that. Or if you were building a Hospital (Lets say 5MW of power) and need to spec out 3-days of power (ie: 360 MWhrs of storage on 5MW Power), you just build a tank that can store a lot of the electrolyte.
I guess... the best way of putting it is that Lithium Ion batteries are like AAA batteries, while a Redox Flow battery could be configured as a larger D battery. D Batteries don't give any more power or voltage than AAA batteries, but are more efficient for energy storage.
It is very easy to imagine how to build a 3000MW-hr 50MW Redox Flow battery (just build a huge storage tank). It is almost impossible to imagine the same with Lithium Ion (I guess you can build massive Li-Ion cells, but note that the Tesla is powered by tiny 3.7V 18650 cells wired up together. So it really hasn't been done before)
Day/Night cycle storage is a low power (Megawatts) high-storage (Megawatt-hours) use case. Lithium Ion batteries are more useful for high-power / medium-storage situations (like frequency balancing, or maybe a couple hours-long storage).
Flywheels are exactly the opposite. They are high-power low-storage devices. Flywheels would be very useful for smoothing out power when birds / clouds come up in front of solar panels (for example). Its easy to build a 300MW flywheel with almost no capacity (only a few minutes of storage). Flywheels could be used when a power-source goes offline suddenly, while a few minutes need to be spent spinning up a new power-source. (ex: Main grid goes down, you need 30 seconds before your diesel generator fully turns on. The flywheel will keep very high-power for the next 2 minutes while things switch over). Although supercapacitors are also a promising technology for this problem.
Different storage technologies for different purposes.
Why wouldn't you keep them at maximum capacity all the time?