I'm not sure that's the best example. In addition to being made in different places, Champagne and Prosecco are made from different grape varieties, and Prosecco is normally made using a different process (Charmat rather than 'traditionelle' - fermented in tank rather than in bottle). They're really quite different products. The generic term that covers both kinds is 'sparkling wine', and if you don't care which kind you get as long as it's good, that seems fine.
Well I do, because even if both taste good, they don't taste the same and I don't want to discover which one I have really bought only after having spent 50€ on my bottle.
If the name has no importance, then why insist on calling your product that doesn't come from Champagne, "Champagne"? And if it has a real importance, then it makes sense to respect it.
Instead of this current racket, where food names become less clear, the regional food manufacturers should be forming associations that build brands. These brands can then utilize logos, trademarks, anti-counterfeiting designs and other enforceable IP to stand out as being "Original Champagne" or "English Cheddar," or whatever is needed.