Jobs are portable, but not taxation and social security contributions :) :)
If you live there for more than 6 months (or have strong relations with the country, even if you spend less months there) you must pay taxes in Italy.
As a self-employed IT worker you have to pay (https://it.wikipedia.org/wiki/Gestione_separata_INPS ) 25.72% of social security which goes into the "gestione separata" (a fund that is well known to be crap, so don't expect anything back) and of course you have no benefit at all from paying this.
Then add income tax, which is another around another 25% (there can be some discount here, for the first years... but it is not that clear as usual in Italy)
So you 'loose' about 50% of your gross income: nothing attractive to me from this side.