It makes sense to write system APIs in C, but there are many more things than system APIs, and many of them find it useful to use C++ constructs.

(edit) Clang's internals are also several orders of magnitude easier to work with than GCC's internals. In fact, clang is designed to be used as a library, and CLIF leverages that very, very highly.

See, for example, https://clang.llvm.org/docs/ClangTools.html . Clang tools are very powerful, and much of CLIF is based on a Clang tool, not a GCC internals hack.