Tool separation and cutting to cut

In quite a few contexts, we find a ruling for a ruling. The Talmud itself also makes this difficult and in several cases answers “It is a ruling” (and so in the Rishonim). And here it makes sense, since as soon as they expanded meat in milk to poultry in milk, they included all the details of the law of meat in milk not to divide between them. See here many exceptions to this rule: https://www.yeshiva.org.il/midrash/26903 Just a note regarding the term ‘separation’ that you used. If the intention is not to cook in the same vessel, then this is not a decree but rather a principle of the law. And even if you do not cook them together, there is ingestion that is prohibited by the Torah in a large enough amount.