I'm a southern girl. No, cornbread shouldn't be dry, unless you are using it in a dressing/stuffing. My family's dressing/stuffing was a dry, no sugar added cornbread, decent white bread in equal amounts, crumbled, uncooked equal amounts onions and celery (though I parcooked them in butter when I started making it), some eggs, poultry seasoning, turkey stock, S&P.
Eating cornbread always had a little sugar, more eggs and oil or butter so it was moist, plus butter on table for those that wanted. Now, I usually add some corn kernels, jalapeños in half for Craig, and sometimes some cheese of some kind.