Just out of curiousity:
What made the plate-mouthed fish go extinct?
I don't think there is a factual explanation since these are species that existed hundreds of millions of years ago in the Cambrian period. The anomalocaris also is resemblingly similar to an animal today, the Mantis shrimp, which although is smaller, but similar, lives on the Great Barrier Reef, it's as ancient as anomalocaris. Both have big raptorial appendages, to hunt prey. So I would think that as these were powerful, large and superior predators, and eventually the prey had to evolve elaborate defensive adaptations as well, like Opabinia with 5 eyes and Hallucigenia with spines on its back, in order to survive. Thus, selection pressures such as these, or possibly even the rise of other predators could have also acted as a selection pressure against them, and over time, the anomalocaris' could not withstand these pressures and eventually decreased in numbers, hence the rate of deaths were higher then births, thus reproduction rates were gradually decreasing, which consequently lead to the extinction of the species over a period of time. I think this is rather reasonable from a logical sense.
edit: more info