Doesn't my analysis of Italy prove lower bound can't possibly be lower than 5x flu death rate, around 0.5%?

No, it does not. Your argument is plausible as an estimator of the CFR, but cannot be used to establish a lower bound.

One reason for that is that you cannot examine just one locality. Some will be high, some will be low -- fluctuations are just the nature of statistics. It is necessary to average the hot spots and the cold spots to estimate accurately.

Basically, this is a really hard problem and the error bars are far larger than most people realize, especially in the media.

Can't you say that at least for Italy as a whole, this is killing 2x as many as the worst flu seasons? Italy has a population around ~60 million, law of large numbers makes it impossible to have error bars THAT big. You'd have to assume that Italians have genetic predispositions to die from COVID-19 far higher than the flu.

> Can't you say that at least for Italy as a whole, this is killing 2x as many as the worst flu seasons?

As I said above, I agree that this argument is plausible. I think your argument is at least as likely to be correct as any other, and probably not too far off the mark for the "true" CFR.

> Italy has a population around ~60 million, law of large numbers makes it impossible to have error bars THAT big

However this is not true. The law of large numbers helps with statistical errors. It does zero, absolutely zero, to control for systematic errors. There are so many factors in play that it is extremely hard to declare anything "impossible" with this pandemic.