Absolutely! I've just been given a huge pile of fantastic old vinyl by my Dad. Beatles, Dylan, etc etc. That he bought in the 60s / 70s when he was around my age. Call me cynical but does really think they'll be handing their kids this year's iTunes Store purchases in 2040?

True, but an artist has several rights in regards to their work.

They have the right to authorise the communication (broadcast, transmission, diffusion) of their music - and, quite separately, the right to control the public performance of their work.

Businesses that play music via a radio, TV or other means are giving a public performance of the music and therefore require permission.