They did flatten the curve[0], they kept their cases within hospital capacity (by banning gatherings over 50, reducing restaurant capacity, having people work from home, etc)
What they never did was crush the curve, which is the strategy most other countries switched to once they realized it was feasible
[0] https://static01.nyt.com/images/2020/03/22/science/11SCI-VIR...
Fewer infected is always good news[1], in Sweden or anywhere else--it means fewer dead now, more infections pushed until later when treatment will probably be better, etc. It's weird to see low infection rates twisted around as if they were bad, "evidence that herd immunity may not be possible". This is particularly true when the prevalence is compared to herd immunity from a model assuming a well-mixed, homogeneous population, which we know overestimates the herd immunity threshold (though not by how much, since estimates of the heterogeneity of the coronavirus are even more uncertain than those of R0).
Finally, herd immunity is a gradual process. Even in a crude homogeneous SIR model, you may approach it asymptotically but never get there. This is good--the only case where a disease "burns itself out" abruptly is when there's big overshoot, which implies many avoidable deaths. Perhaps that kind of overshoot could be desirable in a population of young people, if the small excess mortality in the young people were more than offset by their decreased ability to spread it later; but that's a narrow needle to thread.
For the avoidance of doubt, I believe Sweden did a bad job protecting elder care facilities (though many places that locked down did too), and I disagree with their position on masks. Their response otherwise seems reasonable to me, not obviously better than stricter approaches but also not obviously worse.
1. Unless you know the death count and you're looking for the denominator for your IFR, since more infected then means lower IFR. That was true early in the epidemic, before the first high-quality serosurveys, but not anymore.
The fact that spread in New York has slowed down compared to other states that weren't initially hit hard implies that there's some immunity effect going on.
Nations which have held down infection numbers with shutdowns have, of course, flattened their curves. But they may well suffer from second/third waves which will hike up their total numbers.