But "ginger ale" seems straightforward to me. It's an ale, flavored with ginger. Not even idiomatic, just descriptive. Root beer. Grape soda. Orange chicken.
Ginger ale is in fact, not an ale, it's a soft drink. It is distantly related to Ginger Beer and some variants of Ginger Beer are alcoholic like ales, but Ginger ale was conceived as a soft drink and today continues as a soft drink.
Mass-market ginger ales and root beers are not made that way today, of course.
Dictionaries are also language specific. We don't necessarily expect a 1:1 mapping of words between languages. I have personally always wondered if this subtley shapes thoughts in different languages as well.
I.e. AFAICT, all compound words that defy literal interpretation are idioms. And it's that simple.
The argument then becomes that idioms should be in the dictionary. Some of them are of course, but idioms and slang are a) fast-moving, and b) often dismissed by the sorts of people who edit dictionaries.
At the same time, I am having intuitive issues seeing "hot dog" as an idiom, vs just an ordinary noun. It certainly seems to follow noun rules, and fit into speech as one.
I don't know for sure that it's NOT an idiom though. I could just be wrong here, and have intuition in need of calibration.
So it was an idiom, now it's canon.
Another good one might be "hot dish", which has an idiomatic meaning in the midwestern US, and is slowly spreading. Not sure if it's made it to the dictionary yet. (which dictionary becomes an important question -- I'd expect to see it in M-W before, say, OED)