I believe (correct me if I'm wrong) that the Labradoodle started it all. The original breeder of Labradoodles was doing it for a great purpose though.... he wanted a good blind/guide dog and therapy dog (Lab personality) but non-shedding for people with allergies (Poodle). He came out recently and said he felt guilty that he "started" the whole designer dog fad because that was NOT what he was trying to do. But I think the Labradoodle is, or is almost, considered a breed in Australia. Then everyone else jumped on the bandwagon of breeding everything and their mother to poodles hoping to get the non-shedding fur but it takes years to develop that. Look how long it's taken for the Labradoodle to get where it is. I think cockapoo's are also another that have somewhat more of a breed standard, and a good club behind it. You CAN find reputable Cockapoo and Labradoodle breeders, IMO, they are out there. But most others are just for the hell of it. It's so sad.
I think they became so popular because many people with allergies don't react to Poodles. So the idea of a "Golden Doodle" or whatever became very appealing. People who wanted a Golden Retriever could essentially get one minus the shedding. The problem arises when they get this Golden doodle puppy... keep it for a few months and realize they have more of the Golden retriever hair and they are allergic to it, then bring the dog to the shelter. There is so many poodle mixes in shelters because of this.
In one sense, I can see the appeal in those. But then all the other pointless ones came out... like oh let's breed a Pomeranian and a Boston terrier! Wtf, right. lol