I think adding labels to the product is only useful to a certain extent. There's a few things that stand out, like if a product has 70% DV sodium that's usually a bad sign, or "cheese product" tells you that it's not real cheese (for better or worse). But stopping to look at the ingredient list of every product you buy is time consuming.

This is where online food databases might work better. Scan the UPC/EAN with an app and the app can tell you which ingredients are generally safe, which ones to avoid. The recommendations could be personalized to your dietary needs or allow ratings from different organizations that might have varying criteria for what they consider OK vs bad.

Such apps exist but usually requires someone (volunteer crowdsourcing or paid) to input products into the system so it may not be complete or fully up to date. And as you suggested, supplier information and more detail on the processing isn't available. Having an international, public database of that information (with an API for app makers) could help make nutrition label apps -- or maybe even built into Google Lens -- much more accessible to the general public.