For starters, they have no skin in the game. Unlike local businesses, they don't care what happens, at all. At least the mildly local large companies have some cares about what happens to the country (because they own land, have in-country employees). But the large multinationals basically don't. The number of in-country employees is usually very small.
Second, you have no control over their performance or policy decisions. They can do things that are completely and totally devastating to you (like close down the local branch and stop paying taxes), and you can do nothing, since you have no physical control over anything. Plus, you know, you will now be dependent on their performance globally (this is likely to happen to any sufficiently large company anyway, but ...)
As a result, as you become more dependent on them for tax revenue, government will have to do more and more to appease them to keep that revenue flowing. You have to be very careful, because other than X amount of revenue, you literally have nothing they need. In a country like Italy, the amount of money is not large, so you can't just play hardball with them, because they'll just take their ball and go elsewhere, and you will be left high and dry. If a few multinationals do it, Italy may very well have to run and appease a number of other companies to keep their revenue in Italy.
These are just some of the simple reasons. The short answer is: If you do this, you may as well just hand them your government (or prepare for long term economic hardship).
This is the usual attempt from our politicians, who have no idea how a computer is turned on (no wait.. they play poker on their ipad while discussing laws), to regulat something they do not understand.
If an advertising company really were running some of their operation from Italy, they should certainly pay tax there (and not, say, in Ireland). But you can't expect to tax all ads that are purchased by Italians that really are sold from overseas.
Disclaimer: I'm a Canadian working for Google. And I have no opinion on this particular piece of legislature.
If properly implemented, territorial tax systems do not create a race to the bottom, because countries compete for the quality of service they can offer to businesses that operate there. In theory, a rich individual could live in a tiny country with no income tax, but the moment they tried to put that money to work, they would have to operate in some other country which imposed territorial taxation.
On the other hand, this law is more like a tariff. It seeks to impose a tax on value created (i.e. the selling of an ad to an Italian business) whether or not that value was created in Italy or not.
This is of course, 100% the problem. None of these countries seem to believe they can support themselves long term on the tax revenues earned by just their local people and businesses.
If that's really the case, they are doomed, long term, without changes.
You have such a high tax because of your governments incompetence.
That being said - I'm no fan of that kind of tax avoidance, they should definitely pay their taxes.
But what will happen until the EU has ruled on this (which can take many years), is that Italy will further reduce its competitive advantage because suddenly Italian corporations will be unable to buy Adwords, Facebook Ads and so on which should make them invisible to international customers.
Good luck competing with a startup/small business that cannot buy any ads.