Sunlight and rain decompose wood more quickly, even if that wood has been treated with paint or stain. Over the years I have worked on many homes with small overhangs (under 12in wide), and I can tell you that these unfortunate homeowners are paying carpenters to replace siding on a yearly basis because every time it rains, the siding gets wet, and every time the sun shines, it shines directly on the wood. Trust me, you will be shelling out money left and right if you buy a home with small or no overhangs.
Large overhangs were fashionable in the 70s and early 80s, but by the early 90s, many builders started building homes with no overhangs to give the house an updated look that would sell fast, knowing full well that it would lead to water issues in the long run. If you go to look at a home with any kind of wooden siding and the overhangs are under 2 feet wide…run!