"Flatten the curve" is a strategy that requires logarithmic graphing.
There were 7,468 new cases in NY in the last 24 hours. There were 6,337 in the 24 period before that. That is an increase of 16%. On march 12, when NY becgan shutting down parts of the public and businesses, there were 368 cases. The dozens of new cases in the days following then, would have looked very much the same as the thousands of cases in the last two days. That is logarithmic graphing. That is "flatten the curve". +16% is not a flat curve. If miraculously, for the next 3 days, case growth holds like this and we can see an inflection toward flattening in this curve, we will be seeing 7500 new cases per day in one city, slowly diminishing until there's a fucking vaccine.
If it takes a week for the curve to flatten, we'll be seeing 15 thousand new cases per day. If we're extremely lucky, there won't be another NY. If our miraculus luck continues, and all of these are met, we still have to keep our healthcare baseline above the apex of that curve until there's a vaccine.