I'm astonished that stations don't that already.
They do here. The amount is calculated on the stations turnover, I think. The bigger the station, the more they pay.
Even ordinary businesses that have a radio on in their office/shop have to pay as it's considered a public performance.
That way,the musician gets payed multiple times.
Way back in the 1980's. one of the big pirates here offered to pay performance rights in an attempt to appear legal but it was refused.