You could also make the argument that farmers should use some of their profits to buy insurance against such things. For example, I remember this story about the UK government and insurance provisions from earlier in the pandemic[1], and there were definitely experts on the radio at the time who said that it's possible to purchase cover against epidemics and other rare events - why not for government deciding to eliminate your herd? Or legal insurance so you can sue for compensation?

Additionally, if mink farmers are aware that their animals can be a vector for disease - and shouldn't they be? - then should they not also take steps to protect their own finances from foreseeable events, regardless of their likelihood?

[1] https://www.bbc.co.uk/news/business-51730412