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Farming already is heavily subsidized in every EU country. The whole sector only exists as is precisely because of the fears you point out. And that is perfectly fine, because statistically speaking it already is a rounding error both in share of employment and share of GDP (1.2% of EU GDP), only kept alive for the exact purpose you talk about.

So even if these lobby talking points would be true, and everything had to be 100% subsidized, that wouldn't be a problem.