Because the band can play any song. Only the songwriter can write one. Disclaimer: my daughter is a BMI songwriter.
Disclaimer, BMI “got big” with country western (then called hillbilly music) and rhythm & blues (then called race records) and their hybrid (rock and roll) because ASCAP refused to publish such “rot” (all 3 genres were verbotten at ASCAP). When public tastes went to the publishing firm that DID meet the market demand, ASCAP wrongly blamed payola (when had been in the industry since day one) for no longer having hits on the charts.