There are plenty of CP/M C compilers (I'm planning on including BDS C into cpmish at some point: https://en.wikipedia.org/wiki/BDS_C It's written in hand-tooled assembly!) but with the exception of Hitech C they're all Small C or K&R C. Hitech C works fine, but it's extremely slow and somewhat quirky. CP/M's really a bit small for an ANSI C compiler. (Also Hitech C only targets Z80, not 8080.)
The main reasons for doing this cross-compiled were: that's what I had; life was too short; I wanted something for the cpmish cross-compilation environment _anyway_.
Making cpmish self-hosted would be awesome, though.
Hitech C used to be a free-as-in-beer download from htsoft's website, but it vanished about twelve years ago. I wonder if they'd be open to open sourcing it...