> For better or worse, these names have become generic, a wine maker can't be expected to write "a bubbly wine made in the style of the champagne region, made from grapes bred in the region", you just write champagne on the bottle and don't export to the EU.

IME, most US-produced bottles of sparkling wine that is informally referred to as "champagne" are not, in fact, labeled as champagne. (They are often labeled with terms associated with -- even if not exclusively so -- Champagne-style sparkling wines, such as cuvee or blanc de noirs or brut.)