There was at least one CP/M machine that used tape -- the Epson PX-8 Geneva (an early laptop that had a built in micro-cassette drive). Although it had CP/M in built in ROM and also had the ability to use ROM cartridges like a game console in order to load applications like WordStar.
I have a PX-8. It does work with tape, but very badly --- it's slow even for tape and painfully limited. It emulated a disk on tape, with automatic winding for access to multiple files, and required mounting/dismounting tapes or else you lost data. It was just about good enough for loading and saving Basic programs, but only just. Using it with CP/M is an exercise in frustration.
https://en.wikipedia.org/wiki/Epson_PX-8_Geneva