Instead of three crappy cpus, why not use one decent one?
Well, it was going to be an 8-bit computer, and it was going to have full C64 compatibility which certainly limited the CPU options, but it was also to be a sequel to the C64 (bigger, better, more) so a CPU with double clock frequency was developed (with a "slow mode" for C64 and VIC compatibility) and the CP/M needed the Z-80.
Sure, it was a hack, and the specs was never something the market had demanded/wanted (but neither something that was decided by the developers). The whole computer is improbable, it shouldn't exist. But it does and they got it together pretty well under rather extreme conditions, and it's working (although it was supposed to be able to run CP/M with the VDC chip as well, which would enable the full 4MHz of the Z-80). It's something highly unique, and IMHO it was sort of a suitable end for the 8-bit home computer era, the C128 ended it (some time overdue) with a big bang of extravaganza.
A
Commodore 65 shortly after the first Amiga models should probably have made better sense than the C128, and it could possibly have sustained the 8-bit home computing platform a bit longer (1990 was too late IMHO), but this is in retrospect, and it's easy to be "wise" when looking back with all the answers at hand.