Calculate volume for a proposed auger hole.
Now multiply that by your number of holes in your grid or concentric pattern.
Compare that small volume to that created by trenching or decompacting with an air gun. It's not even close.
Hell, just making a huge new mulch bed with wood chips shows remarkable soil improvements from structural, chemical, to biological aspects in a surprising amount of time.
Vertical mulching/core aerating should be reserved for the circumstances of dealing with a relatively thin and shallow layer of hardpan imo.