That's because you've purchased a private license that allows you unlimited private use. It allows you other rights under copyright law, such as the right to transfer that intellectual property to other media (tape, mp3, etc.), as long as its only used in accordance with private use copyright. It's called "Fair Use."
ASCAP is enforcing payment for public performances, which are not covered by the license you've purchased for personal use. The artists are saying, "If you just want to listen to music in your home, it will cost you this much. If you want to use our music to enhance your business, it will cost you a different amount, depending on what part music plays in your business."
If I play a CD in my home, but it is really a business meeting for my clients and I am using the music to enhance my business, do I owe ASCAP any money?
I don't recall signing that, but I'll take your word for it. You'll probably say something silly like merely buying the CD is agreement to the license. It sort of like sending a check to the city of San Francisco for a dollar, with a inscription "payment in full for the golden gate bridge", then claiming that since they cashed the check it was a sales contract.
Let me cut to the chase here:
The record industry is in a panic now, because they have discovered that they've been selling the wrong thing the whole time. They thought they were selling music, when in fact they were only selling records, and then later CD's. They were selling little pieces of plastic, because nobody's been able to figure out how to make money off of music itself. They only think they're in the music business. No, they're in the little round bits of plastic business, and now nobody really needs the little round bits of plastic anymore.
They're fully correct in being in a panic, but there's a reason that the "R" in RIAA stands for "Recording". It's not the "MIAA", and maybe it should have been.