Re: Italy ... announced a 3 per cent "web tax" on digital advertising
"Presumably there is some reason why simply slapping VAT on digital advertising doesn't work?"
VAT is collected by the vendor (free of charge to the tax authority) but paid by the buyer. If the buyer is a VAT collecting business they reclaim the VAT they paid by deducting it from the VAT they collected before passing that on to the tax man. Ultimately VAT is paid by the consumer.
I've no direct knowledge of VAT on digital advertising but I'd expect it to be charged already; assuming it is it will work in just the same way as VAT does elsewhere. If you buy something that's VATable and digitally advertised you'll be paying your share of the VAT on the advertising, even if you never saw the advert.