A few years ago I saw a show about how Japanese teenagers were (at that time) going through a big reggae fad, and they were getting their hair made into dreads. Which took hours and cost a fortune. So it can be done with straight hair, but I'm sure most of the people we see with dreadlocks have curly hair.
I've seen dreadlocks that looked very attractive, and a few that looked nasty like the ones you described. There's a guy who takes a capoeira class (Brazilian dance/martial art) at my yoga studio who has really huge matted looking locks. I thought he might be Brazilian, but he turned out to be Russian!