I worked for many years at U.S. technology magazines; it may be of interest to readers to see the word-list entries for disc and disk that governed our house style for those words at two magazines that shared the same word list. Here they are, from an era before DVDs appeared on the scene:
disc use for CD-ROMs, audio CDs, and laser discs
disk for floppy disks, hard disks; don’t use diskette
As you can see, the split in spelling that we followed was based not on a general U.S. preference for disk over disc, but on two separable categories of components/media: magnetic/electronic and optical/electronic. I suspect that the split arose because our magazines had gravitated toward hard disk and floppy disk in the early days of personal computers as a U.S. English preference, but nevertheless adopted the conventional spelling compact disc for CDs when they emerged.
Note that this is essentially anecdotal information: I don't know how many other U.S. publishers adopted the same distinction, but my impression is that our house style was not unusual in its treatment of these words.
As for why CDs were designated as compact discs instead of compact disks, even in the United States, I believe that the impetus came from vinyl records, which were usually styled discs, rather than disks, when the term was applied to them at all. That spelling follows in the tradition of the words discophile (since 1940, according to Merriam-Webster's Eleventh Collegiate Dictionary) discotheque (anglicized since 1954, according to MW), disco (the short form of discotheque, since 1964), and disco (the verb associated with disco music, since 1979).