Why not compile to rust or assembly? C seems like an odd choice.
In fact why not simply write rust to begin with?
At times people think C is better. See recent discussion about https://sqlite.org/whyc.html
If I understand the history correctly then it started as a set of C preprocessor macros.
Assembly requires way more work than compiling to, say C. Clang and gcc do a lot of the heavy lifting regarding optimisation, spilling values to the stack, etc