Italian shop owner here (albeit in a field unrelated to tourism)
Before 2018 you could invoice products sold to non-EU customers including proof of non-EU residence, then the customer made the Italian customs office at the port of departure stamp the invoice and send it back to the shop owner for archiving, then we could reimburse in full the VAT, after 2018 the system moved to a convoluted electronic central archive (Otello) that made VAT refund without 3rd party thiefs like Global Blue a hassle for every purchase not of thousands. It is not strictly mandatory to use such services, but the overwhelming majority of shops do.

Solution: in a privately owned shop, tell your problem and just ask for a discount... many times the shop owner is more than willing to do it instead of going through the VAT refund paperwork.

Cheers!