Such a suit could be ignored too, but it would certainly be a PITA for vacationing executives who get locked up in Italy for an outstanding summary judgement.
It's a good thing there are a lot of beautiful parts of the world other than Italy.
I suppose when I asked the question, I am assuming internet businesses for the most part don't isolate themselves to a specific region, so their reply probably makes more sense for the businesses that operate in a small locality. Perhaps they have such a business. I should have considered that prior to asking.
Where this might start to get interesting is if people use infrastructure that is in multiple regions and that infrastructure provider has an agreement to block companies that do not comply. So if AWS for example had such an agreement, then non compliant companies could find their sites broken, even if they are only hosted in the U.S., not that this would ever happen, but it could.
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For larger companies with offices in the EU (especially the ones headquartered there for tax purposes), they obviously have no choice to comply. But what about a small startup, with its only domicile and employees in the US?
What exactly could the EU do to punish a startup in that case? Unless they have some enforceability treaty with the US, I don’t see how they have any legal ground to extract fines for arbitrary laws defined in their jurisdiction. The worst they could do is ask EU ISPs and/or payment networks to block the offending sites, right?