Seems to me like this is a job for Congress—downloads would be protected by copyright laws if Congress changed the copyright law to reflect this.
Whatever law governs copying would govern a digital download. The money was there for ASCAP — they would stand to profit by such acts of copying being called performances — but unfortunately the logic wasn’t there. If Congress wishes to set up a royalty system for such copying, parallel to broadcast licensing, it is free to do so. ASCAP should go cry to Congress that the copyright law is in the stone age.