If I remember correctly, most of these All Elvis or All Beatles stations are temporary - something the owners are doing to ramp up awareness of their (usually AM) frequency with plans for a more mainstream format down the road a few weeks or months.
Does anybody want to listen to one performer or group constantly? In low fidelity monaural sound? I certainly don't. Most listeners would probably tune in for a couple of hours at first, then just hit it for a few minutes after that for a brief Elvis or Beatles fix.
These days, if you're really hooked on any particular group, you have their CDs, or you've downloaded them on your MP3.