For most people (up until we get ahold of them) there are 2 reasons for core aeration: one is to soften the soil and the other is to prep for seeding. Neither of those are good reasons for core aeration. If you have hard soil the solution is to spray on a cheap surfactant. If you are seeding, then that never was a good reason for core aeration. Similarly annual core aeration simply because your neighbor does it, or because your yard guy wants to make his winter boat payments on time, or because your parents did it, or most other reasons, are not good reasons. Grass seed sprouts best on top of the soil where it makes good contact with the soil. In Nature the best seed grows in the hoof prints of grazing animals. We try to simulate that by scattering seed on top of the soil and then rolling it down with a water fillable roller. If you already have a lawn, then the roller effect is not as great because the mass of turf will help keep the roller off the soil. Simply walking on new (unsprouted) seed is as good anything.

Most people don't overseed KBG because KBG is one of those grasses that fills in thin spots by itself. Unless those thin spots are in the shade, it should be pretty dense. If you're trying to 'densify' grass in the shade, then that's a lost cause. You'll need a different ground cover or convert it to flowers. If you have thin KBG in the full sun, then lets talk about that.

Core aeration is a valid practice for some situations but there is not enough information to determine whether it is an option for the OP or not. Spraying a cheap surfactant may be a decent option or it may be a short term solution that you will need to repeat regularly. The two main reasons for core aerating mentioned are well down the list of reasons for me by the way.

My preference is to maintain and develop an ideal and healthy soil that does not require spraying soap on my lawn. I don't visit lawn forums often but am attempting a unique project and have made the rounds recently and am surprised by the closed minded, "Never" ideology. Never aerate, till, top-dress, de-thatch, etc.

If it works for you great. I am impressed by the knowledge many have attained and their willingness to share and help and don't want to minimize that. I am just surprised with the absolute stands taken when there is no way enough variables have been considered to make a mater of fact determination.

There is more than one way to deal with lawn issues, pros and cons associated with those solutions, and enough room for all to pursue the remedies that meet their goals.

Regards