I think the Archimedes did have 4 or 8 'native' channels for audio.

From memory the MOD files included with Lemmings on the Archimedes were 3-channel, possibly leaving one free for sound effects.

I wonder if it was disk space. Lemmings for Archimedes fitted on an 800K floppy; did the Amiga version span to two 720K floppies? Losing a load of samples would certainly be a way to drop the space requirements.