Ironically, the wages of government representatives are also called "diets" in German. I'd say "diet" for "Ernährung" just fell out of use at some point and was reintroduced when diet fads became a thing.

In Danish there's both "en diæt" (what you eat, permanent) and "på diæt" (on a diet, temporary).

I didn't even think about the fact that that word didn't always have the temporary meaning of the word.