> Disperses the herds thereby extending their range,
Thus the vegetation can cope with loses as ever did and not just dies.
> causes some serious (unmanageable) peaks and valleys in populations of prey
Peaks and valleys are caused by diseases and famines, wolves are the worst enemy for livestock and wild deer diseases, so the final result is deer populations more stable and health in fact.
People, specially children, would be also much more safe with wolves than without them, because... first of all, less car accidents with deer, second: less americans killed or having pain by Lyme disease, Rocky Mountain spotted fever, Tularemia, Ehrlichiosis, Relapsing fever, Colorado tick fever or Babesiosis. All tickborne diseases, spread by deer or small carnivores, that are a much bigger threat for children playing outdoors because ticks are everywhere in deerland.
> Apex predator birth rate is low and it would take years to have a noticeable effect
Not necessarily, because the "ecology of fear" change the behaviour of preys. You don't need to wipe out all deer at all. In Yellowstone wolves changed all for better in just five or six years if I'm not wrong.