GCC was implemented in C and there are plenty of other C compilers written in C. GCC has been converted to C++ at some point, but large parts are still essentially C and I do not think the change to C++ was actually helpful (but others may disagree). In any case, the idea that one needs C++ to have C compilers is certainly simply wrong.
Naturally GCC was originally written in C, given its age, and the original GNU coding standards document.
With time, the GCC developers acknowledged the benefits of using C++ over C, and migrated the code.
GCC requires a C++ compiler to bootstrap since around 2012, and GNU coding standards has been updated to several languages beyond C, time to go up with times.
Clang/LLVM with its more permissive licence sees _much_ wider use and is written purely in C++. PlayStation, automotive, platforms and runtimes like Chromium/V8, Android, etc. are all built with Clang.