Here's one of many similar stories to appear every four years. Musician records song. Song becomes popular. All types of people like song. Politician uses song in public assembly. Musician b!tches and moans. Musician accepts royalties from ASCAP or BMI anyway.
Look, there are rules for how to use music at public performances, including campaign rallies. You pay a flat fee to the publishing organizations, ASCAP or BMI, and that money gets aggregated across millions of public performances, and goes to the artists. It's a simple system.
If musicians could decide on how their music could be used in public perfomances, all hell would break loose. A Mormon artist could demand a restaurant serving caffeinated beverages or alcohol not play his song, because he doesn't want to be considered to be supporting something in opposition to his beliefs. An artist who believes exotic dancing demeans women could demand his music not be played at the local gentleman's club. A Green Bay Packers fan could demand his music not be played at Soldier Field.
I suppose you could advocate a law requiring politicians to secure permission from the song's copyright holders, unlike all other public performances, but that would almost certainly be unconstitutional.