That's quite a logical leap you're making there about Italy's healthcare system. China has socialized medicine and they've more or less got the outbreak under control, even according to international observers. Italy now has more deaths than China from the virus and Germany has exponentially lower deaths per capita from Covid than any other country in the world yet all three countries have very similar socialized healthcare systems. Consider the following from an article in Forbes:
"Which brings us to the primary and most striking difference between the German patient population and that of the rest of the world: The mortality rate. Of the 18,610 cases to date, just 46 Germans have died. The most enviable German Covid-19 mortality rate stands at 0.29%, or about 30 times less than that of Italy. That’s a big difference. (Updated: 3/22, 10:45 a.m. Central European Time)"
There are various reasons for this discrepancy in mortality rates between Germany and Italy and not one of them has to do with the fact that both countries have socialized medicine.