The strategy was to face more infections short term in favor of quick herd immunity so it’s actually a very positive sign for the strategy that the death rate is not higher than NYC.
Considering that the curve has flattened and herd immunity is projected in a couple of weeks, it is not clear the total deaths in virus lifecycle will be bad.
I'm not sure why people have seized on Sweden as doing it right, but they will kill about 3.5k extra people compared to Switz (excess deaths). Compared to their northern neighbors they about 8x worse.
All this info at https://www.worldometers.info/coronavirus/ except projections.
If the dire high hospitalization and high death rate theory underlying lockdown was true, you would without lockdown expect worse than NYC death rates in Stockholm because it is very dense and we don't see that.
Moreover, wouldn't number of social contacts rather than population density be a better metric here? Population density is normally a proxy for number of social contacts, but NYC is in lockdown while Sweden is not.