Under the house was a useful space in times past, although it did incorporate some problems.
Today, home-care consultants stress keeping that space dry, laying sheet plastic if needed to prevent dampness from rising from the ground. Foundation vents must be animal-proof and be opened and closed seasonally to seal in heat or provide air circulation at appropriate times. Regular spraying under the house for termites, spiders and possible mold buildup are highly recommended preventive moisture measures. All for a price, of course.
Underpinning was more often seen on homes of moneyed owners, not those of us who were proud to have a roof over our head and a wood floor that was raised above the ground.
Under the house close to the back steps was the perfect place to store garden hoes, rakes, and shovels. Out of the weather, they were protected from rust and damage to the handles. A hoe was handy to grab and meet a snake head-on before he got away. We were more likely to chop a few weeds from the flower bed than if we had to go to the shed for a tool.
A few sawed planks were pushed back to stay dry for building a hog trough, yard gate, or whatever project arose. We put away the croquet set under the edge of the house after a game. An armload of cut stove wood was stacked in easy reach to save a trip to the woodpile when we were in a hurry.
The downside of having no underpinning was that animals could take advantage of the open space too. Hens would scratch a spot and dust their feathers, and sometimes would lay their eggs under the house, beyond reach. My father nailed a flat board against the end of a long cane pole that we used to rake and roll the eggs out after we heard the hens cackle.
Our dogs sought shelter under the house during a storm. They found warmth against the foundation of the fireplace in winter and bumped around against the floor to disturb our sleep all hours of the night.
Puppies and kittens were born under the house and shared their noises.
Wild animals occasionally crawled under the house to die. The odor alerted us. Locating the carcass and getting it out was a major operation.
Once my mother found a roll of small-weave wire fencing not being used, and she tacked it all around the house to thwart animal entry. They would inevitably find a hole or scratch under and then could not figure a way to get out. Same noisy, smelly conditions resulted and had to be dealt with.
Advantages and disadvantages, side by side.