We bow to this fallacy when we set out to govern or model a situation and will not give simple solutions a chance. The fact that laws, in general, now come into being as huge agglomerations of overplanning and hyper-regulation rather than starting out simple and developing naturally in response to arising situations as Common Law did for generations, is a result.
We have faith that a complex problem will naturally only be amenable to a complex set of rules. But this is totally an illusion. In fact those rules create conflicts, and focussing on refinement does not establish coverage of the solution space.
I agree that finding a name is not really all that important. But what is the basic impulse behind the fallacy?
To me the essence of this fallacy is the denial of the experience of theoretical parsimony. We know that vast swathes of science can be captured in extremely simple rules. But we ignore this fact in real life. We are fascinated by the complexity that can come out of a simple statement like Mandelbrot's function, well out of proportion with its meaning. We have a deeply embedded mistrust of simplicity, and we look upon effective simplicity as genius or magic of some sort, or alternately as charlatanry or witchcraft.
The idea that effective simplicity is magic seems to be the driving force behind the faith that we cannot have a scientifically literate population -- that physics is hard, but predicting sports scores is somehow comparatively easy, and we should not really expect people to invest half the energy in learning physics as in analysing football, because it won't pay off.
I think that the problem is that if we accept this kind of explosion of possibilities as a natural thing, we must lessen our faith that we can predict the outcome of the simple rules upon which we make other decisions. This would impede our faith in the ability of law to protect us, and for order to be maintained without ambiguity. So this fallacy is tied up intimately with the "Law of Unintended Consequences", and with the patriarchal racket of throwing your burdens onto the shoulders of someone more competent than yourself and somehow feeling safer rather than feeling unsafe because you are obviously less in control of what might happen.
Plying that psychological impulse as if it were an argument is unfair.
In the interest of practicality, let's not seek a name, but a tactic for circumventing it. Naming a fallacy seldom abolishes it, and often simply derails the argument into an argument about whether this argument was, in fact, an instance of said fallacy.
Manufacturing and computer programming have adopted a framework for combatting this impulse in the form of the notion of agility http://agilemanifesto.org/ which derives from leanness http://www.lean.org/WhatsLean/. The position emphasizes that the ability to adapt to change is the paramount power needed for success, as opposed to strength, endurance or outright speed. And that metaphorical agility, like actual agility, is fostered by awareness of one's state, simplicity of the options entertained, and a breadth (rather than a depth) of experience.
To the degree that this perspective can be injected into an argument, and the scientific approach of experimentation with actual solutions can be allowed to function, the argument can be broken down by demonstration. Solving 80% of the problem quickly in a few steps, can establish the idea that the remaining 20% can be solved without an insane investment in complexity.
In a more abstract setting this often proceeds by identifying a single convention that halves the imagined complexity by applying a simple rule. Since it only takes very few divisions in half to reduce something very large to something quite small, this can interrupt the idea that the very large thing has to be attacked with another very large thing.