The population of the Lombardy region is slightly smaller than that of Wuhan, and they are reporting 3x as many daily deahts as China did during their peak.
One thing regarding the herd immunity response is that it seems to me to become a lot more plausible if you could direct who gets infected and becomes immune.
I did the numbers on the population of Sweden, combining our age demographics with the estimates from the Imperial College report.
With a population of around 10 million, if everyone here got infected, 831 000 patients would require hospitalization and 281 000 patients would require intensive care, which would completely unmanagable. However if only everyone below the age of 40 got infected, 65 000 patients would require hospitalization and only around 3 200 would require intensive care. And that constitutes pretty much exactly 50% of our population. So if it was possible to keep the age of the infected down substantially, it seems possible for a large part of our population to get immunity without completely overburdening the health care system.