CPUs from that era were single core and pretty slow. They had to do everything like game logic, graphics, sound, etc all at once, so it was often resource starved. Sound took some resources, sometimes significant depending on the sound and what else the cpu was doing, unless it was a really simple sound (think NES style sound). Moving that to a dedicated sound card meant the cpu didn't have to worry about sound anymore.

Sound, like a lot of things, could be seen as a peripheral and a lot of peripherals back then needed their own cpu to perform well. One interesting fact I recently learned is the commodore 64 was so resource starved, the external floppy drive you could buy had its own 6502, just like the C64 did as its main processor. It just had to off-load that to another cpu because its own cpu was too busy to reliably run a disk drive. There are other reasons for this like commodore's experience in drives previously was this kind of architecture so they went with what they knew, but its a bit interesting to know your floppy drive was essentially another C64 with its own commodore OS and ram and 6502.