The rigid plastic is tear-resistant and structurally firmer than a paper bill, and those sharp corners work nicely to ride in the groove of a record album, playing music:

Technologically, this is how old gramophones worked — a needle rode the groove, changing the groove’s variations into a vibration in a larger resonator.  The corner of the bill is the needle, and the rest of the bill is the resonator.  Who knew money could be so useful?