Core aeration is the only method I know that relieves compaction without destroying the lawn in the process. Everything else that genuinely loosens soil, tillage or full renovation, kills the grass on the way through. So I will not tell you aeration does nothing for compaction. That claim is wrong, and it gets repeated constantly.
The two honest qualifiers are density and duration. Research counts cultivation in cores per square foot, not in passes. Kansas State puts effective cultivation at 15 to 30 cores per square foot, and a single pass with a commercial spoon aerator, the machine every company in this business runs, delivers roughly half that or less. Two to three passes is what moves the measurement.
Duration is where Giles County clay gets a vote. Our holes close in weeks, not seasons. The clay swells with the next good rain and takes its old shape back.
Then there is the part nobody selling aeration brings up. Genuinely destructive compaction is uncommon in a lawn. Root channels, soil biology, and the freeze-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 tires over the same ground. Most of what gets called compacted soil around Pulaski is heavy clay behaving exactly like heavy clay.