For example, I would think that a general practitioner would have trouble within his field if he did not hold the language to be able to specify what, in particular, was wrong with a patient, even if he knew what it was. Or could he not even be able to understand, say, that a patient was having a heart attack if he did not have the words for it?

The second idea is called strong Sapir Worpf hypothesis. It doesn't seem to be true.

Take a word like aunt. It includes the sister of your mother but it also includes the wife of her brother. Obviously you can separate the two mentally even if you don't have separate words. http://conlangery.com/2013/07/29/conlangery-92-the-sapir-worf-hypothesis/ is a nice podcast that describes it's state.

When you talk about rationality it's still highly useful to distinguish between aliefs and beliefs. There are probably plenty of people out there who don't make that mental distinction. Having different words makes it easier to learn to make the mental distinction.

It also makes it easier to remember thoughts about the mental distinction. Both natural remembering and constructed remembering via Anki.