It is about protecting the consumer, because it prevents a million "grana padano <tiny> alike cheese product </tiny>" type products, like you'd get in markets where these rules don't exist.
Nonsense. Protected origin status is protectionism plain and simple. That's not to say whether it's bad or good, just to call it what it is.
Proliferation of confusing low quality lookalikes is prevented by having an enforced criteria and associated labeling requirements. (If the text is too small as in your example then either the labeling requirements aren't sufficient or they aren't being enforced.)
and if the low quality is really as low quality as claimed, consumer would stop buying it. But if the "low" quality is actually great quality/good value for money, then consumers will buy it - regardless of the naming. Using law to prevent competition is worse for the consumer.
These laws prevent package labeling from informing would-be consumers of the (potentially better) products the imitate. People could know that they have alternatives by requiring imitations to be clearly marked as such. A product clearly labeled as "cheese-style Xheis" suggests that "xheis" is an imitation of "cheese".
Such as brands, there's no real difference in intent between a protected origin and a company brand. And I never heard people complaining why they can't distribute their own Coca Cola either, even if it's up to the standards.
In fact the similarities are even stronger when you realise that some protected origins are very small in size and that you have bigger Coke factories than some protected origins.
It doesn't really protect anything except the name. Parmesan is protected, my local supermarket sells it right next to cheese that is not called Parmesan. I have yet to be arrested for buying the cheaper one.