Aren't all lawns decorative?

There is value in tick control around a residence. For that, grass is the most practical ground cover. Anything beyond the bare minimum is an excess.

Wouldn't dirt, sand, or rocks work just fine?

Not if that dirt grows tall weeds. Many lawns don't need to be irrigated at all.

Where I live in the Northeast, the natural state of a patch of dirt--or for that matter a patch of gravel--will be to become a forest in most cases by way of grass, weeds, bushes, and trees.

To some degree. But there are a lot of reasons to keep some sort of buffer around the house in any case. Now (unless required by local regulation/HOA/etc.), this doesn't necessary mean a perfectly manicured Kentucky bluegrass lawn but in a lot of the country just letting nature take its course will have tall grass, bushes, and eventually trees growing right up to the foundations.

Midwest ground becomes a lawn without any real effort. Maybe seed it a bit.

To imitate that in the southwest you usually need irrigation.