Nobody’s stopping you from making your own Parmigiano wherever you want, you just can’t call it that, because the name acts as a quality guarantee for the consumer.
So they are stopping me from doing that. If I can't call something what the consumer expects, I can't make the thing the consumer expects. Because that's what this discussion is about: these kinds of labels should be only for quality, not for region of production. I am not advocating for dropping the label or handing it out everywhere.
Unless you're trying to tell me the cheese is necessarily of worse quality in a way that's not physically measurable just because it wasn't made in the same region, the region label adds exactly nothing above a purely quality-based label.