The Z80 was a secondary processor in the C128. The main processor was the rival MOS8502, a descendent of the Z80's main rival, the MOS6502.
The Z80 was included so that the C128 would be able to run CP/M software which was considered to be an important inclusion at the time.
CP/M was supplanted by the ubiquity of IBM-compatible PCs and MS-DOS, which is a shame considering that MS-DOS started life as something deliberately quick and dirty based heavily on the syntax of CP/M. The dir command? That's from CP/M. The peculiar *.* wildcard syntax? Also from CP/M.
Now, it's true that CP/M took a lot of inspiration from Unix and similar, but it wasn't trying to replace Unix. MS-DOS though? Arguably, it came to fill the same niche that CP/M already occupied. Except everyone was then on x86, not Z80.