I believe it's the latter - a fast spread will overshoot past the minimum herd immunity, while a slower spread won't, thus resulting in fewer overall deaths and ICU visits.

In other words, shrinking the area under the curve while flattening the curve.

Of course, that's a highly simplified model, might not be true, etc., etc. But it gives me, a leftist, some support for my belief that some "social distancing for as long as it takes" is a more reasonable viewpoint than no social distancing.

(I replaced "strict" with "some" because I prefer the Swedish model - see https://news.ycombinator.com/item?id=22768170 . I just haven't a clue for how things will turn out.)