Alternatively, you're reversing the causality. As such fallacies have become borderline ubiquitous in many relevant aspects of life, greater appreciation and understanding of what's happening led to the emergence of language that's not only more figurative and visual, but also more precise. Because while all motte and bailey fallacies will be false equivocations, not all false equivocations will be motte and bailey fallacies.
Engaging in a genocidal action and then claiming it's self defense when scrutinized is a textbook motte and bailey fallacy. Claiming that people who oppose said genocide are supporters of fringe radical elements within the genocided, is a false equivocation, but not a motte and bailey fallacy. Indeed, you could make your exact argument about association fallacies, or a wide array of other fallacies for that matter - as most tend to involve false equivocation at some point.