It's not bougie at all, all regional and traditional food produce is heavily regulated here (in Italy) and I think you'd struggle to find anyone that thinks rules about product naming should be relaxed. Traditional cuisine is just super important to Italians and they take the idea of foreigners undercutting their producers very seriously. It isn't just famous cheeses like parmiggiano either, every area has its own unique food and wine.

Coming from a lot of other countries it seems weird and stuck up because we're used to eating food that's been extruded or precooked on an industrial scale, but I think it's endearing that they give a shit about food heritage. Local food is just a huge deal here, people care about eating locally sourced foods and seasonal vegetables.