The definition of "wallflower" in the idiom dictionary is wrong, or at least incomplete.
The idiom dictionary has:
WallflowerMaybe it means that in some other parts of the world, I don't know. But it does not mean that in the USA and Canada.
A woman politician given an unimportant government position so that the government can pretend it takes women seriously is a wallflower."
I suggest this definition:
(1) A person who shows up at dances and parties, but who, because of shyness or unpopularity, does not dance or socialize. (2) A person or organization that hopes or tries to be interact and participate, but is generally ignored.
Definitions 1 and 2 immediately below are the meanings we would intend in the USA and Canada when we use the term wallflower. Definitions 3 and 4 are unfamiliar, and they are not idioms anyway.
wallflower definition | Dictionary.com
Definition 2 below is very familiar idiom. Definitions 1 is unfamiliar to me, and they not an idiom anyway. Definition 3 is a broadening of the classes of wallflower, and a broadening that I'm sure most North Americans would instantly understand.
1. a person who, because of shyness, unpopularity, or lack of a partner, remains at the side at a party or dance.
2. any person, organization, etc., that remains on or has been forced to the sidelines of any activity: The firm was a wallflower in this year's bidding for government contracts.
3. a European plant, Cheiranthus cheiri, of the mustard family, that, when growing wild on walls, cliffs, etc., has sweet-scented, usually yellow or orange flowers, but when cultivated has flowers varying in color from pale yellow to brown-red or purple.
4. any of several related plants of the genera Cheiranthus and Erysimum.
wallflower - definition of wallflower by the Free Online Dictionary, Thesaurus and Encyclopedia.
n.1. a. Any of numerous herbs of the genus Erysimum of the mustard family, having fragrant yellow, orange, or brownish flowers.
b. Any of several perennial herbs of the genus Cheiranthus, especially C. cheiri.
2. One who does not participate in the activity at a social event because of shyness or unpopularity.
3. A security, company, or industry that is out of favor with investors.
Word History: The sweet-smelling flowers of Cheiranthus cheiri came to be called wallflowersCounty Ball. ... Although originally used to describe women at dances, the word is now applied to men as well and used in situations remote from a ballroom.