We only have the data on the age of deceased, not the place where they died

Negative, the numbers in Italy show in the vast majority the deceased in hospital. Several that died at home are not counted either (due to what majors told the press). Homeless will be missing in the stats even more.

Lets see how it develops in Russia. From the numbers they are at the beginning, likely 2,3 weeks behind Italy. I do really hope no heavy countermeasures are necessary. But I would not bet on it.

And the result of destroyed public health system.

The PHS has never been better in (northern) Italy. Still many challenges to be adressed besides Corona, but with the increasingly old society it is no easy task.
Lets see how countries like Germany handle the crisis. If their hospitals are crumbling as well.. it shows that modern medicine may hit its limits sooner than we would like to accept.

P.S. And of course it should be no free way ticket to elimitate privacy/human rights. But I am very confident that the Democracies will prove to be resistant at least to this level of pressure.