Moreover, I believe the earlier versions of rustc only output LLVM, so you need to bootstrap a C++ compiler to compile LLVM anyway. If you have a C++ compiler, you might as well compile mrustc. Currently, mrustc only supports rustc 1.54, so you'd still have to compile through some 35 versions of it.
None of this is practical. The goal of Dozer (this project) is to be able to bootstrap a small C compiler, compile Dozer, and use it to directly compile the latest rustc. This gives you Rust right away without having to bootstrap C++ or anything else in between.