I grew up in the antiwar movement and participated in my first sit-in when I was 12. Sit-ins are a sort of denial of service, but that's not why they work. What they do is convey the message: "I am willing to put myself in harm's way for my beliefs. I am willing to risk arrest and jail. This matters." This may not be convincing for people who strongly disagree with you, but it makes an impression on people who haven't been paying attention. Discovering that your neighbors are willing to be harmed, arrested, imprisoned, or even killed for their beliefs is a striking thing.Moral Suasion
And that's a crucial difference between a DDoS and a sit-in: participants in a sit-in expect to get arrested. Participants in a DDoS do everything they can to avoid getting caught. If you want to draw a metaphor, DDoSers are like the animal rights activists who fill a lab's locks with super glue. This is effective at shutting down your opponent for a good while, but it's a lot less likely to draw sympathy from the public, who can dismiss it as vandalism.