Core aeration is the only way to relieve compaction without wrecking the lawn in the process. Everything else that genuinely loosens soil, tillage or a full renovation, kills the grass on the way through. So I will not tell you aeration does nothing for compaction, because that is not correct either.
Two qualifiers matter. The first is density. Research counts cultivation in cores per square foot, not in passes, and K-State puts effective cultivation at 15 to 30 cores per square foot. One pass with a commercial spoon aerator delivers roughly half that or less, which means two or three passes before anything measurable happens. I laid out the core density numbers here. The second qualifier is duration. Maury County clay swells, settles, and takes its shape back, so our holes close in weeks, not seasons.
Then there is the part nobody selling aeration mentions. Genuinely destructive compaction is uncommon in a lawn. Root channels, soil biology, and the freeze and thaw cycling a Zone 6b to 7a winter delivers all work against it year round. Real compaction is nearly always something people did, the same feet or the same tires over the same footprint. Most of what gets called compacted soil out here is heavy clay behaving like heavy clay, tight when it dries and hard underfoot in August. Cores will not turn clay into loam.