Anybody anywhere can produce Buffalo Mozzarella. The protected term in the EU is "Mozzarella di Bufala Campana" which has the region already in it's name. The scheme has been introduced as trademarks protection of such terms that often have been associated with a specific region for centuries is not possible. It's really no different than regular trademarks for modern brands. Historically those schemes were introduced over a hundred years ago after faked products misled consumers. It's also a weaker interference in the free market than copyright protection: Anybody can start producing Mozzarella di Bufala Campana in the region while the rights to Kraft Cheese belong to a single company.

Producing a product the cheapest way possible is not the end goal. If those cheap products drive the traditional way out of the market (as consumers have no reliable way of distinguishing products) consumers that specifically want the product from that region are harmed. All others can buy generic Buffalo Mozzarella produced anywhere just fine.