Because it's not just equivocation. Read more of the actual original definition/usage of motte-and-bailey.

Motte-and-bailey isn't just an argumentative form, it's also a political strategy. It's people pushing/doing controversial thing A but every time they get called on it they bring up uncontroversial thing B. Or, they even retreat to thing B, but then when the pressure is off they come back out and start pushing/doing thing A again.

"Equivocation" covers a wide variety of situations, but motte-and-bailey is more specific and includes the notions of a strategy executed over time which includes action.

You haven't actually described any differences between the terms. (Well, you did claim one, that "motte-and-bailey is more specific", but combined with your appeal to "actual usage", that is clearly untrue.)

Motte-and-Bailey speaks to equivocating about positions in argument. There are many other ways to equivocate, e.g. over the meaning of a single word, used in multiple ways in the same argument, as opposed to a retreat to an easier-to-defend position over the initial one presented/being discussed - as in the thread above.

The relationship between the two words is akin to the one between “rectangle” and “square”.

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.

The original SSC article about Motte-and-Bailey used "strategic equivocation" as an alternate name, not just plain old equivocation. I.e. intentionally equivocating whenever is convenient for some political/social/whatever goal