We do have some tuning knobs though, including vertical risk-stratification, which has collected dust around the world.
It is possible to have a much more acute and accelerated course among the least vulnerable populations while isolating the more vulnerable populations.
Whether Iceland and New Zealand will be viewed as successes depends in part on how much misery is inflicted during the long period it will take to finally reach herd immunity in those places, and how many people in vulnerable sub-populations are infected along the way.