If you shift the curves over and account for population, Italy's actually about a week behind China in locking things down.
The sad thing is that even after locking everything down, you expect case numbers to continue to rise by ~100x (which is what happened in Hubei), as people get past the incubation period, infect the people they're living with, medical workers fall sick, and so on. So the only right time to impose a lockdown is before it looks like a problem at all, which is politically impossible to pull off.
They are very clearly trying to balance public health with economic losses.
It certainly doesn't help that Milan citizens are ignoring restrictive measures, bars are offering free drinks to "restart the normal life", and companies are attacking the government for the lack of profits because "it's just a flu". Meanwhile hospitals are getting swamped and are calling for selection of who should or should not have access to ICU.
The sad thing is that even after locking everything down, you expect case numbers to continue to rise by ~100x (which is what happened in Hubei), as people get past the incubation period, infect the people they're living with, medical workers fall sick, and so on. So the only right time to impose a lockdown is before it looks like a problem at all, which is politically impossible to pull off.