If you cannot compile GCC with a C compiler, it isn't C.
It is true that GCC is not written in C anymore, but it is easy to see that the code is still relatively close. I am also myself writing a C compiler in C at the moment and there is no problem at all.
Quite curious about which commercial C compilers, written in C, are being sold, keeping those companies in business.
Every year thousands of CS students write toy C compilers.
GCC and Clang aren't "sold" either, nor is MSVC really.
I have never contributed to GCC, but as a fact I have visited plenty of files from its source code, and so far haven't encountered any meaningful use of C++ that couldn't easily be rewritten in plain C. The overwhelming majority of the code would probably compile as C without changes.
I'm sure that there are far more meaningful "problems" with the architecture of a compiler written in C that are not the implementation language. For example, GCC is a pain to build (IIRC when I tried many years ago, I gave up).