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.