As previously stated, Mother Courage is already musicalized to perfection. To transform Mother Courage into a musical rather than a play with music would most likely destroy the point of the play. Brecht feared that plays/musicals could create empathy for almost any character depending on how they were depicted, which resulted in his famous "alienation" techniques, of which Mother Courage is the product. Mother Courage is not supposed to be a sympathetic character, and the use of actual songs (by Duke Special or most other composers) would only water down the powerful anti-war message of the play (which is the actual point of the show, not the tragedy of Mother Courage). The reason "Threepenny Opera" and "Happy End" work so well is the collaboration between Brecht and Weill, how they worked together to create the desired effect. I wouldn't say it could never work as a musical, but it would be a very specific composer with a very specific book writer/adapter.
"Sticks and stones, sister. Here, have a Valium." - Patti LuPone, a Memoir