re: Why don't most houses in Louisiana have gutters?

The purpose of gutters is to divert water away from the base of the house. You need them when you have a basement to avoid water seepage through the foundation walls of your basement, especially if you have a finished basement.
As there are typically no basement in the New Orleans area they don't serve a purpose. My house in Baton Rouge had a partial basement which was always flooded.
And houses in areas that get a lot of snow typically won't have them as the weight of the snow and ice will rip them off the house