It would be better for students to know the origins of idioms, for it would help them to grasp the meanings of them; however, the origins of many idioms are obscure, and many have lost their origins in terms of etymology, so for those idioms, students have to learn them by rote.
Being in an international environment, I am very cautious of using idioms because the non-English mother tongue people really have no idea about the meanings or origins.
I try to discourage people using idioms in multi-lingual environments because of the issue of understanding. So would it help knowing the origins of idioms of different cultures? Yes, but idioms are really of interest only within the culture and less so across cultures because they often don't mean anything when literally translated. So they would never be used outside of that culture.
FYI: This is something mother tongue people don't really understand when using idioms in their language with non-mother tongue attendees. English or otherwise.
Below are some interesting translations of idioms
French
The idiom: Avaler des couleuvres.
Literal translation: “To swallow grass snakes.”
What it means: “It means being so insulted that you’re not able to reply.”
The idiom: Sauter du coq à l’âne.
Literal translation: “To jump from the cock to the donkey.”
What it means: “It means to keep changing topics without logic in a conversation.”
The idiom: Se regarder en chiens de faïence.
Literal translation: “To look at each other like earthenware dogs.”
What it means: “Basically, to look at each other coldly, with distrust.”
The idiom: Les carottes sont cuites!
Literal translation: “The carrots are cooked!”
What it means: “The situation can’t be changed.”
Other language connections: It’s bit like the phrase, “It’s no use crying over spilt milk,” in English.
German
The idiom: Ich verstehe nur Bahnhof.
Literal translation: “I only understand the train station.”
What it means: “I don’t understand a thing about what that person is saying.’”
The idiom: Die Katze im Sack kaufen.
Literal translation: “To buy a cat in a sack.”
What it means: That a buyer purchased something without inspecting it first.
Other languages this idiom exists in: We hear from translators that this is an idiom in Swedish, Polish, Latvian and Norwegian. In English, the phrase is “buying a pig in poke,” but English speakers do also “let the cat out of the bag,” which means to reveal something that’s supposed to be secret.
Japanese
The idiom: 猫をかぶる
Literal translation: “To wear a cat on one’s head.”
What it means: “You’re hiding your claws and pretending to be a nice, harmless person.”
The idiom: 猫の手も借りたい
Literal translation: “Willing to borrow a cat’s paws.”*
What it means: “You’re so busy that you’re willing to take help from anyone.”
The idiom: 猫の額
Literal translation: “Cat’s forehead.”
What it means: “A tiny space. Often, you use it when you’re speaking humbly about land that you own.”
The idiom: 猫舌
Literal translation: “Cat tongue.”
What it means: “Needing to wait until hot food cools to eat it.”