I tried a NEC, Sony, and Toshiba IDE ATAPI CD-ROM drives, and I have a Amiga 4000 040, Kickstart 3.1. I had AmigaDOS 3.1 at the time.
I had to install the atapi.device and mount the CD0: with that device and it worked perfectly. I tried AsimCDFS, AmiCDFS and CacheCDFS and unless I used atapi.device it would not work. Am I the only one that needed it? I remember being told by everyone on USENET that it would not work with stock scsi.device.