But we need to remind also that a very fast collapse, would not left a trace on the DNA. A Pompeii like event couldn't be disclosed just with DNA changes.
Are you sure? I thought there were at least two ways to estimate population size from DNA: Y chromosome (since it is only passed father->son), and mitochondrial DNA(since it is only passed mother -> child).
Why wouldn't those show up with a very rapid population collapse?
Very fast collapse typically comes with positive evidence of this as people leave their lives out in the open, expecting to return later. Eg see the Roanoke colony in Virginia.