I've also never understood the appeal of DD. We only got one in town in the past decade or so. It was a thing in CT, but my grandparents weren't the eating out type, nor did they bring home donuts, so I never had much exposer to the brand (hell, I've never even been in one of their stores) until I started working at the kennel. The bosses occasionally go get donuts and such.
The donuts aren't bad, but, IMHO, nothing to write home about either. I'm guessing the larger appeal is to coffee people.
I think Cville had a Starbucks before we had DD. Since I never really did Starbucks, DD wasn't really in my radar. If I wanted coffee or tea, I went to the local coffee joint, The Mudhouse.