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.
The meaning is more fluent. The doctor can put you on a strict diet with a mealplan "lægen har sat mig på en streng diæt med kostplan og det hele", that isn't necessarily temporary.