But the comment you reply to explicitly points out the process is in fact relevant as it is itself a cultural artifact. You're not replying to their main point.
How are the customers hurt if their pie has not been baked by a babushka in Petrozavodsk using the old original recipe, but by an anonymous migrant worker in a dark kitchen using an optimized recipe if the end result is objectively the same? The packaging doesn't have to say who it was made by.
I also don't see the problem with the heritage. The comment I replied to already said anyone could call their pies Karelian, so there was no restriction that benefitted the residents of a specific region. I can see a PDO-like carveout that goes "we want to preserve the traditional pie-making of Karelia, so we want this activity to remain economically viable. Therefore, only pies baked in Karelia can be sold as Karelian pies." But I don't see how Sysco baking the same pies and distributing them nationwide helps maintain the heritage.
Even if you make something that tastes and looks exactly like the original, you still can't call it Specific Thing because the process wasn't followed as it's an integral part of the product. Think of it like a trademark. You can't create some brown sugary stuff and sell it as Coca-Cola - even if it tastes EXACTLY like it does.
Nothing about this is about profit or economic viability, it's not even a small part of the equation. The purpose is to preserve cultural heritage and not dilute it with shitty imitations calling themselves something they are not.
The issue is how this will be handled in law. Can the law define this in a way that is not overly strict or overly permissive? The current attempts is effectively the law doing this, but with an overly strict approach of what counts as 'objectively the same' by judging the process and not purely the outcome. Would it be possible to make the law's definition of this more permissive, to focus only on the product produced, without accidentally becoming overly permissive?
Think of it this way. Nobody would eat a Karelian pastry and not care that it's Karelian. That's why they're eating it, otherwise they'd just eat some other pastry without the cultural weight.
It's the same thing with paintings and sculptures. The painting has value because someone thought it up and put the time to make it. And you view it not for the colors, but what they mean. Why did they choose to paint this? What was going through their heads? What is their perspective?
If you just shoot out a painting, it has no value, because the value isn't the painting. It's your take, your perspective, and the painting is a tiny window into that.