“Punctuated Equilibrium” is not a new concept.
Species are relatively stable until some perturbation of their ecosystem disrupts the viability of the dominant lifeforms in whatever niche they fill.
Extinction leaves a gap which is rapidly (in geologic time) filled by evolution of previously stable local or invasive populations, i.e. advantageous mutations allow a new group to take over the role left open by the extinctions.
Think dinosaur extinctions opening the door for mammals to become dominant in a world where reptiles previously occupied the apex roles.
(Also think the rapid extinction of Christianity in Europe, allowing a wave of invasive predators intent on Conquest and extinction of everything European or Christian.)
I think punctuated equilibrium is generally accepted. However there are a lot of detail to be filled in and beyond this study, details to be filled in to flesh out the how and where. Smaller extinction events are just now being found.