Marc Lavoie, page 265 of Post-Keynesian Economics: New Foundations: "In fact, the SFC approach is perhaps a misnomer, as several other theories relate stocks and flows in a consistent way. The peculiarity of the post-Keynesian SFC aporoach is that its models truly integrate the real and monetary sides."
In other words, do not focus on the name "stock-flow consistent models," the (alleged) contributions go beyond stock-flow consistency.
The usefulness of SFC models depends upon your theoretical perspective.
If you are already a post-Keynesian economist, SFC models appear to offer a rigourous, standardised framework for setting up economic models. One of the problems facing post-Keynesian approaches is that there are considerable differences of opinion in how to approach economics, and the mathematical models used appear quite different.
The hope was that some of the distinctions might disappear if cast into the same mathematical framework. In practice, there remain considerable differences in the behavioural equations between various post-Keynesian schools of thought, so SFC models have not been able to completely unite the various schools of thought. (The text by Lavoie discusses this at greater length.)
If you are not post-Keynesian, the usefulness depends upon your views about mainstream macroeconomic models, which I will summarise as dynamic stochastic general equilibrium (DSGE) models here as a shorthand. Please note that there is a massive number of variants of DSGE modelling; my comments here reflect the views of an external observer who is not worried about the distinctions between those models.
(Since SFC models have an explicit economic model structure, they are not comparable to unstructured models that are generated by a statistical fitting procedurs.)
From a post-Keynesian perspective, DSGE models embed a great many assumptions, pretty much all of which have been criticised. For example, utility maximisation, the production function, rational expectations, general equilibrium, representative households, price determination, and even the distinction between randomness and uncertainty have all come under attack by post-Keynesians. (Since "DSGE models" vary, not all of these assumptions appear in all models. However, it is probably safe to say that almost all "DSGE models" incorporate at least some assumptions that at least some post-Keynesians object to.) SFC models do not embed those assumptions, and so have an advantage if you view those assumptions as incorrect.
However, even if you move past the arguments over the assumptions, the tractability of SFC models is an advantage versus pure DSGE models. Standard DSGE models have to make simplifying assumptions in order to remain tractable, such as not having a financial sector. Although certain DSGE models can relax such assumptions, what typically happens is that only some of them can be relaxed at once.
In practice, many central banks have had to use hybrid models, that only incorporate some behavioural equations taken from DSGE theory. Although it might not meet a purist's definition of a "SFC model", you could easily create such a hybrid model from a SFC model base. From the perspective of applied mathematics, I would be hard-pressed to give a formal mathematical reason why such a model is not a member of an extended family of "SFC models." (It would not be classified as a DSGE model, as there is no assumption of equilibrium. The behavioural equation is just a bolted on assumption, independent of equilibrium arguments.)
However, if you insist that macro models must reflect the optimising choices of households, SFC models are not going to help you very much.
