There's really no reason to do so if your soil is compacted, either. Everything you can do using aeration can be done (better and more permanently) in another, less invasive manner.

I can only think of two exceptions to that. Aeration can be useful to even out a bumpy lawn if you rake the cores around into the lower areas from the higher ones. Over time, it can even it out without disturbing the lawn overmuch.

The second case is for a resource tapped and/or organic depleted soil. The aeration cores can allow some of the nutrients or very late stage organics deeper into the soil immediately without waiting for the resurgence of the soil life to do it for you. But that's usually a once and done thing, and not required. It's always an option to simply wait and let nature do it for you.

Agree.

Furthermore, homeowner soil is almost never compacted. Livestock producer pastures can become compacted when they allow the livestock onto an uncompacted soil when it has been raining steadily for several days. The livestock hooves walking onto soggy soil push the air out of the soil. When it dries, you have compacted soil. Adobe bricks are manually compacted soil bricks.

Golf courses can become modestly compacted because they have money to make. They allow golfers to walk on the turf even when it is soggy from rain. Football fields can become compacted for the same reason (not golfers, though). Football fields have a stampede going on, so the soil can become compacted very quickly.

What homeowers get, which the TV commercials and lawn care "experts" convincingly call compaction, is hard soil. Hard soil is caused by the depletion of fungal population and their hyphae in the soil. Hyphae are the strands of stuff that fill up your bread bag when you really let the bread sit in bright light for too long. They are microscopic, but when they fill the bag you can see them more or less as a green fog. In a bread bag you can have hundreds of miles of those microscopic hyphae. In a lawn, you should have millions of miles of hyphae. When they get moist they swell slightly and push the soil particles apart. When they dry out they shrink slightly allowing air to penetrate deeper into the soil. Also when they are moist they become spongy. When you walk on healthy soil, it should feel spongy. When that soil dries out in a few days, it should become rock solid again. That's normal.

"If my soil is not compacted, is there any other reason to aerate"

Yes.