Athanasius notes that before the incarnation humanity was under the dominion of false gods, enslaved to corruption and idolatry.  The Word took flesh to deliver us from that slavery, and the form of that deliverance was an act of worship: “in this body offering Himself for all, He might deliver all from false worship and corruption, and might Himself become of all Lord and King.”

This is fitting enough to satisfy Anselm: False worship inverted by one single act of sacrifice.

Augustine and Aquinas say similar things.  Alongside the satisfaction theory, we might place a “liturgical” theory of the atonement.