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.