They're looking in the Bluffton area, which is near Savannah, GA.
Coastal area, sandy area, slab houses. It is not unusual.
My conclusion is gutters are not a bad idea but not required as much in places with basements.
Yes.
A diverter above the door is helpful if you have no gutters.
Upstate is different than coastal.
It is a trade off. Cleaning gutters with pine needles is a pain. Upstate, the pain is worth it, especially on sloped lots with a basement or crawl space. It helps to have a drain that collects the downspout output and and discharges it down slope.
I'm in NC on a sloped lot. Yes, we have a basement. Basements in the Carolinas are "walk out," such that one side is basement, the other side is at grade. It is very good to have gutters on the upslope side, with water diverted through drainage pipe past the house downslope.
As mentioned above, if you don't have gutters, try to do something under the drip line, such as a rock/gravel area, otherwise you'll carve out erosion.
BTW, one problem with all of this non-gutter area is
if you have a deck attached to the house. In my opinion gutters are crucial in that case. Otherwise, you get constant splash back from the deck to the house siding. This happens even without rain near the coast. Dew drop off the roof occurs through the summer and early fall. This will eat your siding and even framing under the siding. I've worked on enough disaster recovery projects like this to see the damage to houses and decks without gutters to verify they are pretty much essential in this case.