If a 5kW unit would be prohibitively expensive or large for my example scenario, then different materials and configuration for the ion exchange unit would be needed.
Note: I am not worried about the size of the pumps and tanks. These could be stored underground, in the case of a suburban house. For apartments, this would be harder to retrofit. Above paragraphs in this comment are all about the ion exchange unit, which would determine the maximum charge/discharge rate.
But granted 5kW is not a big problem.
I've suggested before that some site such as Electrek have a monthly column, "1, 5 and 10 years ago in battery announcements", so we can look back at the hype. There are so many of these "sort of maybe works in the lab, trillion dollar industry next year" announcements. Usually with videos full of stock photos and talking heads.
You can imagine that there is appeal to being able to store energy year-round, not having to deal with price regulation and energy companies.
My point is, a situation can arise where people want nothing to do with the grid unless there is no other way. Back in the day, running a steam turbine with coal in your backyard was not practical. So was dedicating an entire room for a mainframe computer. When things get miniaturized, running them in your home becomes possible.
If these flow cells, which have been around for a very long time, would somehow be practical in a scaled down form, I can see it work in a one-per-building configuration, assuming those buildings have solar panels.
However it may be preferred to either run the flow cells on a centralized grid as you suggest, or to provide it a more local level, e.g. one installation per residential block. Because people in apartments also need power.