Italy actually has a standard for electronic invoicing, and most companies are required to use it ("Fattura Elettronica"). It works by having a centralized portal to which invoices are submitted.
EDI is only semi-standardized; in my experience usually each pair of trading partners requires a separate effort (usually the bigger partner imposes the requirement and the smaller one has to make changes). Some difficulties include:
* There are multiple protocols for exchanging EDI documents (AS1, SMTP, FTPS, SFTP...)
* There are multiple standards for the documents themselves (EDIFACT, X12, GS1 XML...)
* There are partner-specific business rules that need to be set up (this partner needs an ASN, that partner requires invoices to be for only one PO each, the other partner can only accept invoices which use their ERP’s internal codes...)
Some of these problems can be papered over with a “VAN” that can translate between standards, but I have yet to see one business send a non-PDF invoice to another without a lot of fuss.