I sympathize with US ranchers, but I agree with the courts that "Product of the USA" okay... M-COOL (Meat Country of Origin Label) is the right solution... and let me give an example why: If I buy a new, real wood, kitchen table, that was imported as a sapling, planted in the USA for 20 years, then milled in the USA, then worked into a table by USA craftsmen -- would that be a product of the USA? I'd say so, and I th…
If I were to show you the jar of (blended) honey I have in my cupboard, it lists every country it came from. I haven't looked at any soup I have (granularity with stuff like that is more important when it comes down to food standards in individual blocs), but anything with differing food standards would likely be marked as such. Anything that's a mixed source of raw product has to be labelled as such, such as "Made in Ireland from a blend of EU and non-EU sources".
One of the good things about the EU, though I'm sure some in a particular ex-EU country might debate this, is that any food imports are required to be of the same standard as anything produced within the bloc.
Regarding the term "product of the USA", I think the problem there is down to phrasing: the table is a "product of the USA" if the work done in the US to transform it from the raw material to a table is done in the US. Maybe the solution is to do the same thing as is done in Europe, and have something like "Product of the USA from US and non-US raw materials".
[And if you want complicated, try being somebody working in Northern Ireland right now! Though it's a mixed, mostly positive, blessing for them: they can operate under "made in the UK" (good domestically, less so abroad mostly), or "made in Ireland" (so long as they're sticking to EU rules, and NI is so dependent on agriculture that it's to their benefit, as with tourism, to export under an all-Ireland umbrella), but it makes the paperwork... fun.]